Гармониялық тербелістердің кинематикасы
Маятник тербелісінің осциллограммасы мынаны көрсетеді: егер үйкеліс күші жоқ болса, маятниктің амплитудасы тұрақты қалып, ал ығысуы синусоида заңымен өзгерер еді. Бұл ұйғарымның дұрыстығы маятник тербелген жағдайда қайтарушы күш синусоидасы өзгеруінен дәлелденеді: F=mgsinα. Демек, осы күшпен маятникке берілген үдеу де синусоидалы өзгереді: .
Тербелістердегі энергия айналуы. Еркін тербелістердегі энергия айналуы
Маятникті орнықты тепе-теңдігінен шамалы α бұрышқа бұрайық (6-сурет). Мұнымен біз маятникке қосымша потенциалдық энергия береміз:
Wp=mgHe.y.
мұндағы He.y маятник көтерілуінің ең үлкен мәні.
Маятникті қоя берейік. Ауырлық күшінің және реакция күшінің әсерінен маятник тепе-теңдікке ұмтылады. Тепе-теңдік жағдайында оның потенциалдық энергиясы кинетикалық энергияға айналады:
Мұндағы жіпке ілулі тұрған дене қозғалысының жылдамдығының ең үлкен мәні. Сол жақ қалпының шетіне жете отырып, маятник қайтадан кері бағытта қозғала бастайды.
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hMTIyBo/ny5Wvfvr1MQwO6iEQA7MyzZ8+MPswmq9sXX3yheenl5bV79+5GjRqZMaKvr6+YbitWrMh+F5iHh8eOHTvMewC0yBEtUb16dTc3N60lVrrOnDkjXySKjIw0cPSzzz6Tb4IK0EUkAmBnRC4kyj4D4e7u/uuvv5qXhwQi95PPnodcXV3Xr19v9oYYIh+ubUlyEhJb1apVja4WknU50dGjR3M6JMS1oUOHyjc0oItIBMDOmLSVepbly5e/9957Zo8oZlJKy4IFCyy56PPkyRMx3Yzev2ZYaGioFSNRYmLiqVOncjrap0+fEiVKyDQ0oBeRCICdMTUSjR071sJVujdu3DCpf79+/fr372/JiPfu3RPTrVSpUpaMEhISEhERYbjPpUuXUlNT3dzcLBlIr927d+d02c7b23vSpEmSjwgYRiQCYGdMikRNmjT59ttvLRzR8CpgLbVr1164cKGFI4q53czFxcXCeRQxK6yF1CJ8w2vWrGnJQHpt3Lgxp0MjRowQ88goQFpEIgB25uLFiyJ75suXb+XKlSKfBpSTjIyMK1euiOzs5eX1888/u7pa+qP1+vXrRvsUL17cwl3ig4OD8+bNm5iYaLhbZGSk5JHowYMHO3fu1HuoZMmSEyZMkHY4QAwiEQB7Ehsba/RXuMacOXMsvLQkuHbtmsjFzoJp06ZZvk2pEBfEfMbsO7iZRwiLQtY5cuSI4W5yLCeKiIhIS0vTe2j27Nne3t6SjwgYRSQCYE/EXzUTftn36tXL8hHFT0oJYWjIkCGWjxgVFSWmW6VKlSwfKzQ0VPlIFB8fn9O1xaZNm3bo0EHa4QCRiEQA7In4SDRr1ixJRhQfiWbOnOni4mL5iJcvXxbTzfLpKJW45UTC9zw9PV2Sj5Zl3rx5eh8y6eHhsXTpUqlGAUxFJAJgT0RGojp16ojZOVWMS5cuielWpUqVdu3aSTKiyEgkySxRSEiI0T7JyclRUVFVq1a1fDjBw4cPc0qr48ePz9qpF7AKIhEAeyIyEg0cOFCqEUVGokGDBik8YnBwsOVjBQQEFCpUyOhjkM6cOSNVJJowYYLelVIVK1ZkVTWsi0gEwG6kpqYa3bxd4Onp2bFjR0lGTEtLE3MHvpubm4QblIpZS+Tr61uyZElJhgsJCdmzZ4/hPpGRkT169LB8rBMnTqxevVrvoSVLlri7u1s+BGA2IhEAu3H58uWcblPKrl69eh4eHlKNaHQXMFXmipy8efNKMuKDBw/i4uKMdpNkiiiLULzRSCTJCuuMjIyBAweq1WrdQ927dzd78xNAKkQiAHZD5FUzs/cyM3tEqdYtiR+xcuXKUo0oZoX1uXPnhChj4ROeFi9efPbsWd32/Pnzz54925IzA5IgEgGwGyLjQrVq1ex3xPPnz4vpJmEkErPC+tWrV9HR0ZYs6H78+HFOe3TMmDHDws3aAEkQiQDYDZEBpUqVKgqPKNXSY/EjSvgZCxQoULZs2Zs3bxrudubMGUsi0ejRo1++fKnbXr9+/T59+ph9WkBCRCIAdkNMXPDy8ipXrpySI3p4eEh467jIWSIJI5Eq89qZmEjUtWtX885/5MiRNWvW6La7urouW7bMvHMCkiMSAbAPL1++vHv3rtFuQUFBFi55yT7inTt3jHarVKmShXuNaaSnp4t5KFGBAgWKFi0qyYhZQkJCNmzYYLhPZGSkeScXPlROTygYOXKkhFcAAQsRiQDYB+WvYYl8brWEEzbR0dEpKSlGu0keI8SssNa7MlqMefPm6X3SUkBAwOTJk807JyAHIhEA+2CzC4nsesQstWrVcnFxSU9PN9Dn5cuX169fN/Wi5P3797/88ku9hxYvXuzl5WXS2QBZEYkA2IfcEFCsspBIlbkAKzg42OjnPXPmjKmRaOTIkXqfVR0eHt66dWuTTgXIjUgEwD7YbCSy69vNNEJDQ8VEIpO2qT9w4MDGjRt12318fObPn29afYD8iEQA7IOYlT1+fn4lSpRQckTht3vp0qWlGtG6kWj58uWG+5j0DOvU1NTBgwfrPfT1118XL17chOIARRCJANiBO3fu6H2qjRYJ1x3fvXv3xYsXSo6YkJBw69Yto92EMCEkP6kG1RDzwEaTItGsWbOio6N122vVqiXhFrmAhIhEAOyA8jd/2ex1OjmmiFSZl/+8vLySkpIM9Hn69Ont27fFzIoJEXbatGm67c7OzhEREVI9swCQFpEIgB3IDQHFWmurs7i4uNSoUePYsWOGu505c0ZMJBo2bNjr16912wcNGlSrVi0zSwRkRiQCYAdyQySy7iyRKvPamZhI9MEHHxju89tvv23btk23vXjx4l9//bW51QGyIxIBsAM2G1AkvN3MurNEKnEPbDS6nOjNmzdDhgzRe2j+/Pk+Pj7mVAYogkgEwNalp6dfuXLFaLciRYoUKFBAyRELZZJkRJW49VJOTk7y7YAhyQrr6dOn37hxQ7e9devW4eHhZlYGKIJIBMDWidzmQvmNNSQc8fbt22JuqStbtqx8T3wuX758/vz5nz9/bqDPw4cPHzx4UKxYMb1Hb968OWPGDN12b2/vxYsXS1MlIBsiEQBbZ7NXzex6RL1CQkL++OMPw33OnDnTpk0bvYeGDBmSnJys2z5p0qSAgAAJ6gPkRCQCYOtyw1OkHSASbd++fc+ePbrtQs0jR46Upj5ATkQiALYuNwQUq6+tzmL2CuukpKThw4frtjs5OUVERLi68rsGdoB/pgBsnZiAIu2649wQwvQyOxJNmzZN76O3e/fuXb9+fQkqA+RHJAJg0xITE8VscxEQEJAnTx4lRyxdurRUt5Snpqbq3ftCi5ubW2BgoCQj5qRIkSIlS5a8e/eugT537tx5+vRp9pv7YmJiZs2apduzUKFCeldbA7aJSATApl28eFGtVhvtJuH0ifIjXr58OS0tzWi3ChUqCKlIqkFzEhoaajgSCSIjI9977z3Ny8GDB+u9QW/27Nn58+eXuD5ANkQiADYtN1zDspGFRFmESLR161bDfc6cOaOJRJs2bdq3b59unyZNmnTv3l36+gDZEIkA2LTcEIlsZCFRFpMe2Pjq1Su9d5N5eHhERERIXBkgMyIRAJuWGwKKTc0S1a5d29nZOSMjw0AfTST68ssv7927p9th/PjxFSpUkKU+QDZEIgA2TUxAcXV1rVSpkpIjuri4BAUFKTmiSqlI5OPjExgYePnyZQN9bt68GR8ff/fu3Xnz5ukerVix4oQJE+SqD5ANkQiA7Xrw4MGzZ8+Mditfvry7u7vCI3p4eEgy4vPnz+/fv2+0m5eXV7ly5SQZ0aiQkBDDkUitVkdGRk6dOlXvqvAlS5ZI9Z8DUBKRCIDt4qqZRlBQkJOTk1SDGhYaGrp69WrDff773/+ePHlSt71bt25NmzaVpy5AXkQiALYrN0Qim7pqlkXMAxv15qH8+fPPmTNHhooAJRCJANiu3BBQbGptdZZq1aq5u7vrfdSQYdOnTy9UqJAcJQEKIBIBsF1s+CrHiEa5ubkJqej06dMmvatevXp9+/aVqSRAAUQiADYqIyPD8CLfLJ6enuXLl1d4RAnvML948aKYbkpGIlXmCmuTIpGrq+uyZcvkqwdQAJEIgI2KiYlJTk422k3CdcciR6xUqZKzs7MkI964cePVq1dGu+XLl69kyZKSjChSaGjokiVLxPcfOXKkwqENkByRCICNyg3XsEQuJKpcubJUI4okZoW1RkBAwOTJk+UrBlAGkQiAjcoNkcgGFxJlCQwM9PX1jY+PF9N58eLFXl5ecpcEyI1IBMBG5YaAYrORyMnJqVatWocOHTLaMzw8vHXr1gqUBMiNSATARuWGgGKDd+BrhIaGGo1EPj4+8+fPV6YeQG5EIgC26PXr1zdu3DDazdfXt1SpUgqPWLp0aUlGTE5OvnbtmpieVolEISEhRvt89dVXxYsXV6AYQAFEIgC26NKlS2q12mg3CdcdW2VEwxvOa1StWvXtbIKDg93c3KQqIydGV1jXrFlz8ODBcpcBKIZIBMAW5YarZiJHFDx69GhfpqyXrq6ugYGBWfGodu3azZo1k6qk7EqWLFm0aNGHDx/qPers7Lxs2TKpHkYA2AIiEQBbZLMBRfmFRLrS0tIuZVq3bl2jRo1kikSqzGtnO3fu1Hto0KBBtWrVkmlcOcTFxR0+fPjQoUP//vvv48ePnzx58ubNGz8/P39/f+G/aZ06dVq2bKn8ww5gU4hEAGxRbohE4meJDDDpAUJmnFxvJCpevPjXX38t37jSOnDgwMKFC3ft2qV7mfJxpitXrmzevHnMmDH16tX7/PPPrX4DXceOHYV6DHTo16/f0qVLTTrnxx9//Msvv+i2u7i4/PHHH02aNDGtRAdFJAJgi2w2oNhaJBKzCNpsOeWt+fPn+/j4yDeuVI4cOTJ06FDxs3HHjx9v27atkEiWL1+eJ08eWWszICoqynAHoU5Tz5nTNyE9PX3ixIl///23qSd0SEQiALbo0aNHDj9iTst0bIfevNW6devw8HDlizFJXFzcyJEj16xZY8Z7N27cePfu3d9++81ase+ff/6JjIw88b/u3bun1eHixYuJiYl58+YVf87t27cPGzZM75zfv//+a1G5DoRIBADQz8/Pr3z58tmfFODl5bVo0SIrliSGkCc+/PBDIdZotVetWrVfv37NmjULCAjIyMi4cuXKypUrly5dmp6ertXz2LFjw4cPX758uVIl/x+enp4NMmW9LFOmzO3bt7N3EIo/depU06ZNxZ9TOImQioQ4u3fvXq1Dvr6+FhbsMIhEAIAcXb161dolmGbNmjWfffaZ1va9QsiYN2+e0J69sWamsLCwTp066Z7np59+6t+/v6zXJUUSKtRdBiSENpMiUZYvv/xSNxJVrFjR/OIcC5EIAOAgVqxY0bdvX63nSxUtWnT79u05hZsOHTrs2LFD79JjIRXZbCQyYzmRKoenapkRrRwVkQgA4Ah+/vnnzz77TCsPlShR4u+//zb8wPE+ffrojUSHDx+WtkLzNGrUSLfxxIkTZpwqKSlJt7Fly5ZmnMohEYkAAHZPiC+ffvqp1m323t7eO3bsMLoBS40aNfS237lzR7L6LFCpUqWCBQvGxcVlb3z+/Hl0dHRgYKBJp9L9ROXLl69bt66lJToKIhEAwL49ePCgS5cuuqukV61alVPcyU5ITnrbnZycJChOCmFhYb/++qtW4/Hjx02NREePHtVqYUuW7IhEAAA7plarO3XqpPsMhfBMYs4gJCq97QEBAZYWJxG9kejYsWM9e/Y06Tz79+/P/rJQoUJ9+vSxsDZHQiQCANixZcuW/fXXX1qNvr6+CxYsEHkGIVvobX/nnXcsqkw6QiTSbTR1hXVcXJzW7Wbjxo3LaYYsdyISAQDs1bNnzyZOnKjbLvyyL1asmMiTrFy5Um/7p59+anZh0qpRo4aPj09CQkL2xqioqPj4ePFPFVq9enVqaqrmZZkyZbhqpoVIBACwV5MnTxZSkVajkBIGDRok8gxHjhz5/fffdds//PDDmjVrWlqfRJydnevVq/fHH39kb1Sr1SdPnmzevLmYM7x582bOnDnZW6ZPn+7u7i5llfaPSAQAsEtxcXF6HzA9YMAAkXMnwhn0LscpVKjQwoULLSxPWo0aNdKKRKrMS34iI9H3339///59zcuGDRt27NhRyvocApEIAGCXIiIitJ5Srcq8Tax///5i3v706dNWrVrFxsZqtXt7e2/ZsqV48eKSFCkVS5YTJSYmTps2TfPS2dl5/vz5klXmQIhEAAD7k5aWtnTpUt32evXqiblT7OzZsx06dLh+/bpWe758+bZt29awYUNpqpROaGioh4fHmzdvsjeePHlSzHu/+eabx48fa1726tVLzLMJciEiEQDA/hw8eFDvzfNdunQx/MaEhAQhIsyZMyf7WuMsVapU2bJlS4UKFSSrUjpCHgoJCdG6t+7ly5dRUVHBwcEG3nj79u158+ZpXvr6+mafMUJ2RCIAgP3ZsWOH3va2bdvm9BYhQkVERCxatOj58+dah9zd3ceMGfPFF1/Y8orjsLAw3ccNHD9+3HAkGjduXPbLixMnTixcuLAs9dk/IhEAwP7s3LlTt7FkyZK6V83u3bu3d+/eTZs2HThwQPcJ1y4uLl26dJk6dWqZMmVkKlUqjRo1+vbbb7Uajx071rt375zecuLEiQ0bNmheli9fftiwYXLVZ/+IRAAAO3PlyhW9G5DVr1//8ePHDx8+vHHjxtWrV8+dO3f69Olr167pPUnBggV79OgxZMgQo5ug2Qjh0zk7O2vt42Z4hfWIESOyv5w9e7abm5ssxTkEIhEAwM6cPXtWb/vGTIbf6+/v37p1644dO7Zs2dLV1Z5+Cfr4+FSrVu3ff//N3hgdHf3ixQs/Pz/d/uvWrcu+/vq9995r166d3EXaNXv61wAAgOD8+fMm9S9QoEBISEhYWFjjxo3r1Knj7OwsU2Fya9SokVYkUqvVJ06cEOKdVs83b95MmDBB81IIf3PnzlWiRHtmUSQSYml8fLxUpRiwbNmyvn37KjCQTAICAvTO8VqoSZMmBw4ckPy0AGDjLly4oLfdw8OjUKFCRYoUKVasWNmyZcuVK1exYsWqVauWKFFC4QplIqQ63UcKHT9+XDcSzZ49+/bt25qX/fv3DwoKkr0+O2d+JBJ+xyuTh1SZN0YqM5AcEhIS5MhDgsqVK8txWgCwcTn9UI2OjraXhUHm0fvARt1tax89ejR9+nTNS39//y+//FLeyhyC+ZHo0qVLEtZhmF3/7pfvG2X4xksAcFQ5/UFeoEABhStRWKFChQIDA4Xkl73x1KlTarXayclJ0zJx4sTExETNy6lTp+bPn1+5Ku2W+ZHo4sWLEtZhQMmSJcXv9GuD5PtG2XVSBACzvXz5Um+7t7e3wpUoLywsTCsSJSQkCL9oqlatmvXy/PnzP/30k+ao8JtC5A4nMD8SCd/iatWq/Z3p5MmT2QOphYQMFBQUFBwcHJTJ3n/xf/zxxyEhIVeuXLl8+XLW/8bExOjuyyOGi4uL8N2o87/s/TsDAOYRQoDe9oyMDOHnpMLFKKxRo0Y//vijVuPx48c1kWjkyJHZb9SfN2+e/S4nV5j5kShv3rzNM6ky/xWeO3fu7/919+5dkScR/u2WLVs2K/poMpBwZrOrskEeHh7VMmla1Gp1bGxsVkLSRKWnT5/qfXuJEiU0Gah27dq54W8gADDM09NT79/hQlTSezu6I8lpOdFnn32mynyC5cGDBzXt7du3b9asmXLF2TlpbsIXEmiNTIMHD1ZlXs3VfVy6Xu+///6WLVskqcGOODk5lc3UunXrrJYTJ07Ur19ft2eDBg2OHj2qbHUAYOv8/f31RqLHjx87fCQKCAgoVaqU1gLzrAc2pqWljRkzRtPo7u4+a9YspeuzZ7I8l6h8+fKnT58W0zOnh4oqY9OmTVmxWpU5tdijRw9rVTJ79my97ePGjVO4EgCwfUIkyn6HucbVq1crVqyofD0KCwsLW7t2bfaWmJiYp0+f/vLLL8J3QNM4fPjwcuXKKV6dHZMlElWoUEFkJLp+/bocBYj0zTffaNbomfrgLwnFxsb++uuvuu3BwcEG9i8EgFxL+E2v9wHWp06dyg0/NnUjkWDPnj1Tp07VvCxSpMjEiROVrcvuyTVLJLLn69evHzx4UKxYMTnKMOz3338/d+6c5mVUVJTyNWSZN2+e1p41WbLPfwIANOrXr6930cW2bduyxwJlCH/bT58+Xfid8vjxYyGItG7dWvjp/dZbb8k3YqNGjXQbhw4dmv1GPOFvfskX5ir/SRUm1yyR+M7Xrl2zSiTK/hgrweXLl5WvQZV5K+mKFSt020uUKNGtWzfl6wEA29egQQO97RcvXvzzzz/feecdxSrZsWNHly5dkpKSsl7euXNn2bJlP//884YNG9q0aSPToEFBQQULFoyLi8vemD0P1apVq1evXtIOapVPqjArzxKpMiOR3vXzsjp16pTwf5vsLcJ/3devXyt/P5fwT0rvIsERI0bY136EAKCY2rVr6y4xzjJ69Ojjx4+b8fMzLS1t1apVixYt2rZtW0BAgJi3CL+/sqcEDeG3SadOnc6fPy/fDErDhg2FOnM6qrvph4Ws+EmVZBOzRHLUYNi3336r1aJWqy9fviwkayXLEP4fuHDhQt12Pz8/zbpvAIAWZ2fnwYMH670BJTIy8tNPP129erX4s8XHxwthaM6cObdu3RJe9unTZ9++fWLeOGPGDN2UkEXICt99993SpUvFl2GSsLCwnCJR586d9d7CbAkrflIlyRKJ/P39hV/qL168ENNZ+Uh05cqVHTt26LYrH4k2bNhw79493fYBAwY42MOZAEBaffv2nTZtmt6dPdasWRMXF/fDDz8Y3e31xIkTQjfhR7Hwez2rpWDBguPHjxdZw++//27g6J49e0Sexww5XV3x9vaeOXOm5MNZ8ZMqSa5LM+JvOlM+EglpV61W67Yrv5xI+KNEt9HT03PYsGEKVwIA9kX4w3vp0qU5rbncu3dvpUqVPvjgg/Dw8KCgoCJFivj6+iYlJQl/q8fGxkZFRZ08eVL4Na/1R2mTJk1WrVpVsmRJkTU8evTI7KMWqlmzpvCXs+66i7Fjx4qvXzwrflIlyRWJxD+aSOH78IX/A+jeu5hF4Uh0+PDhf//9V7f9k08+KVy4sJKVAIA96tKly8GDB5cvX6736KtXr37JJOZUQrz46quvhg4dmn3zVKOEpGVgtwbhqPhTmcrZ2blevXpaF/hKlSolRCI5hrPiJ1WSjLNEInvGx8c/efKkUKFCMlWiZfbs2ampqXoPKXwfvt7HMwr/ykePHq1kGQBgvyIiItzd3S1ZyCL81O3UqdPMmTONXmXT1bJlS93txjTkvg+rUaNGWpFI+BSenp5yjGXdT6oYGWeJxHe+du2aMpHo+fPnP/zwQ05Hr1+/LqQlNzc3BSqJjo7We/H1o48+MulbBwC5mYuLy+LFi6tVqzZ27Fi964oMcHV1DQ8P/+KLL4KDg80bfcKECevWrXv16pXuobx588q9/YDWcqKGDRsK2U6msaz7SRVj/VkiVWYkqlevnkyVZLdw4UK9/0WzpKenx8TEmP3/DZPMnTtX73ommeY8AcCBffbZZx07dpw1a5bwQz4hIcFo/8qVKwvpoU+fPkWLFrVk3LJlywpBQTiV1t1Y3t7eGzZsEHknv9mEP601Xzs7O8+bN0++saz7SRVjK7NEMpWRnfAfUu8d79lFRUUpEImePn2q9wbRJk2a1K5dW+7RAcDx+Pn5ff311xMnTvzjjz8OHz589uzZ2NjYuLg44Se/u7t7/vz5hfRTrVq1WrVqvffeexJOxrdt2/bcuXPffPONMO6TJ0+KFCnSokWL8ePHy725mPC5pkyZonnZq1evmjVryjqitT6pkuSKRAUKFLC1+/B//PFHIYsY7qPMCuslS5YkJyfrtjNFBACW8PT0fD+TkoMKAUvvJgSymjNnzoMHD7K+zpcvn5BUFBjUKp9USTI+H1n43v3zzz9iesbExMhXRpb09PScdpvPToFIlJKSsnjxYt124c8XIXHLPToAwN7FxcVlf/jQpEmTFLtFybHJGIkqVKggMhIpcB/+2rVrb9++bbSbApHo559/fvz4sW47U0QAADE+//xzzZKpwMDAIUOGWLcehyHvLJHIns+fP3/27Jm/v798xYh8mmd0dLRarTbpuRSmmjt3rm5jQEBAx44d5RsUAOAYzp07l/1RTPPnz2dDTKnIO0skvvO1a9dCQ0NlqmTnzp2XLl0S0zM5OfnmzZvybV+3d+9evU8/GjVqlIuLi0yDAgAcg/BHe//+/TMyMrJedujQ4b333rNuSY7EJmaJVDJHohkzZojvfPnyZfkikd71TAUKFOjdu7dMIwIAHMbSpUtPnjyZ9bWPj4/eyw4wmw3NEslUxl9//XXs2DHx/aOiomR6EOeFCxcOHDig2z548GAvLy85RgQAOIwbN25k35L2yy+/LF68uBXrcTwyRiIbuQ9/+vTpJvWXb4W13ikib29vIRLJNCIAwDFkZGR8/PHHmn1ea9SoMXToUOuW5HjkXZMl/j58mSLRxYsX9e6bYYBMkejhw4fr16/Xbf/000+F7CjHiAAAhzFu3Ljjx49nfe3m5vbTTz85OztbtyTH4+CRyNQpIpVskWjhwoUpKSlajS4uLqNGjZJjOACAjZs5c+b48ePbtWu3fft2wz2FAJT9OsPkyZPffvttmavLjeSNROKXE8XFxcXHx/v6+ko4+q1btzZu3Gjqu4Qy7t+/L+0F2qSkpIiICN32jh07OszWMAAAk1y4cEH43/Pnzxvutn79+n79+mleNmrUaMKECfJWllvJPkskvvO1a9ek3aJl1qxZaWlpZrzx8uXL0kYiIeA/f/5ct53HM9qsixcvinnceS4xePDgWrVqWbsKwNFkRSLhr/eEhAQfHx+9fZYtWzZo0CDNXfdFixYVEpKsD8/LzWxllkgldSSKi4szeysWIRI1a9ZMqkrUarXeDYpbtGhRrVo1qUaBtO7du7dq1SprV2Er2rZtSyQCpCX8xX7lypWsr4VsVL9+fa0O8fHx/fv3z74I1cPDY/PmzUIqUq7KXMa2ZokkHHr+/PlJSUnmvVfv0xTNtn37dr0fjSkiAMi1oqOjNQtM+/XrN2HChLCwMCHupKenX716ddu2bYsWLRL+ttf0d3Z2Fv5O001OkJC8kahgwYL58uV7+fKlmM4SRqLExMQlS5aY/XZpV1jPmTNHt7F27dpNmjSRcBQAgB3JumqW5dKlS927dzfQ2cnJ6fvvv2ffJ7nJvjFK+fLlIyMjxfSUMBItW7ZMd+2Or69vfHy8mLdLGIlOnz79119/6bYzRQQAuVn2SGSYh4fH6tWrO3ToIGs9UCkQiSpUqCAyEsXExEgyYmpqqu7aHeGf1KRJk0aPHi3mDI8fPxYSVf78+S0vRu8SXSEmhoeHW35yAICdMnqjWZaKFSuuX7++evXqMpeD/6HELJHIno8ePXr16lWePHksHPHnn3++d++eVmPPnj2bNm0q/iRRUVENGjSwsJLbt29v2bJFt11IZtwvAAC5mdFZIj8/v5EjR44ZM0b4k16ZkqDELJH4zteuXbPwJiy1Wv3dd99pNbq4uAj/qooVKyYEEaGDmPNcvnzZ8kg0f/789PR0rcYiRYr06NHDwjMDAOza4sWL//7773Pnzt24cePhw4eJiYkZGRne3t7FixevXr1669atw8PD8+bNa+0ycxcbmiVSSRGJfv311+joaK3Gjh07Zm1uHxAQEBsbK+Y8li8nSkhI+PHHH3Xbhw4dSuQHgFyuTSZrV4H/w+ZmiSwcbsaMGbqNmq2Dg4KCFItEP/zwg5CKtBqFyD9w4EALzwwAACQneyRS8j78Q4cOnT59WquxdevWVatWzfpaiES//fabmFNZ+Gii9PT0BQsW6LZ/9tlnwnfDkjNDGY0aNZJqvb8DKFasmLVLAADZyR6JVAreh693k1fNFJEqMxKJPNWdO3dev37t7e1tXiWbN2++ffu2VqObm9uIESPMOyEU5uXlVa5cOWtXAQBQjuNEon///Xffvn1ajQ0aNGjYsKHmpfhIpFarr1y5YvYGI3rvve/atWuJEiXMOyEAAJCVEpFI/HKi+/fvJycne3p6mjGK0SkilSmRSJV57cy8SHT06NF//vlHq9HJyWnMmDFmnA0AAChAoVkikT3VavX169crV65s6hDCu3SfAFS1alWt9fz58+cvXLjw48ePxZzT7BXWenfwECoJDg4274QAAEButjVLpMq8dmZGJJo5c2ZGRoZW47hx43R7BgUFyRqJhPp37typ2663GAAAYCNsa5ZIZdZyokePHq1evVqrsWzZsp07d9btLESiP//8U8xpzYtEc+fO1Q1n9evXt/zBjwAAQD5KRKJChQqJ33LVjEgkpJA3b95oNY4ZM8bZ2Vm3s/jlRNevX09NTXVzcxNfyfPnz1etWqXbziavAADYOCUikSpzoujMmTNiepoaiYSkFRERodVYpEiRXr166e0vPhKlpaXFxMSYtABo6dKlr1+/1mqsVKnS+++/L/4kAABAeQpFogoVKsgUiZYsWaI7/zR8+PCcNs0w6aazy5cvi49EqampixYt0m3nRjMAAGyfcrNEInveuXMnJSXF3d1dTOc3b97Mnz9fq9HX13fAgAE5vaVEiRI+Pj66W23oFRUVFR4eLqanYO3atQ8fPtRqLF68ePfu3UWeAQAAWItys0Qie2ZkZNy4caNSpUpiOq9cufLRo0dajQMHDhRSkYF3CSfX3fdDL5NWWOu9937EiBEmrUYCAABWYXOzRKrMa2diIpEQnmbNmqXV6OnpOXz4cMNvDAoKkjwS7d+//8KFC1qN+fLl69evn8gzAAAAK7K5WSKV6OVEmzZtun79ulZjr169ChcubPiN4pcTRUdHq9VqJycnoz317uAxYMCAvHnzihwLAABYkUKRSI778GfMmKHV4uLiImYts/hIlJycfPPmzbfeestwt6ioqN9//12r0cPDY9iwYSIHAgAA1qVQJFJJfR++EEHOnj2r1dipU6cyZcoYfa+pN50ZjUR6VxF98sknRYoUET8QAACwInuNRLqbvDo5OWlt8pqTcuXKubu7p6SkiOksRCKtjdK0PH78+JdfftFqdHZ2Hj16tJjzAwAAW6BcJBK/nOj27dtpaWmurjnWdurUKd1NOVq3bl2lShUx5xfyilDMpUuXxHSOiooy3GHRokW6z87+4IMPTFo+BQAArEvRWSKRPYU8FBsba6C/7hSRYMKECeKLCQoKEhmJDN90lpycrPvsbBWbvAIAYG9scZZIlXntLKdIFB0dvX37dq3Ghg0b1q9fX/z5xS8nMhyJVq1aFRcXp9X4zjvvhISEiC8GcGxi7tkEgJyo1WplBrLFWSKVweVEM2bM0P3umDRFpDIlEsXHxz948KBYsWJ6j86dO1e3kSkiQIM8BMBCwo8RZVKRcpGocOHC4nfSyCkS3bt3T3ct89tvv92qVSuTijHpprOoqCi9kWjXrl1Xr17VLaZly5YmFQMAAAxQJhUpF4lUmRNF//77r5ieOUWiOXPmpKamajWKvNEsu8DAQGdn54yMDDGdL1++3KxZM912vY9nZJNXAADskaKRqEKFCpZEoufPn//www9ajW+99VbHjh1NrcTT0zMgIODmzZtiOutdTiR8EN273oRzdu7c2dRiAACA1Sk9SySypxBWMjIynJ2dszcuWrQoMTFRq+eYMWO0uokUFBRkSSTSO0U0YsQIFxcXM4oBAAA5cbS1RCpTbjpLTU29detW2bJlNS1JSUkLFy7U6la0aNGePXuaV4wQifbs2SOmp+6jie7du7dx40atRn9//z59+phXDOCoRO4SCAA5ccA7zlSm33SWPRL9+OOPure7Dx8+3MPDw7xixK+wfvz48fPnz/Pnz69pWbBgQVpamla3wYMHe3t7m1cM4MAU+3EGAJaw0VkiVWYkat68edbX6enpuvuI5cuXb8CAAWYXY+pOZ5rnHiUmJn7//fdaHby8vIYMGWJ2MQAAwLoUjURm34e/bt26W7duaXUYOHCgcDazizH1PnxNJFq+fPnLly+1Onz66acFChQwuxjYmpMnTw4fPtzaVdiKb7/9tnHjxtauAgDkpWgkUpl7H/7MmTO1jnp5eVn4G8vPz69IkSKPHj0S01mzwjojI2P+/PlaR11cXEaNGmVJMbA1L168EFKRtauwFU+fPrV2CQAgOzuIRLt27bp48aLW0V69ehUqVMjCYoKCgkyNRFu3bo2NjdU62qFDhzJlylhYDAAAsCKlI5H45USaO+RnzJihdcjV1VWSJyIKkejw4cNiemoike6SJsHYsWMtLwYAAFiRFWaJRPZMTk6+c+fOrVu3/v77b61DnTp1CggIsLwY8cuJbt++/fr163Pnzp04cULrUPPmzatXr255MQAAwIpsd5ZIlXntTHdWxsnJyYwdPPQSH4nUavWVK1f0Pp6RTV4BAHAAtjtLJNi2bZvu0xTbtm1buXJlSYox6aaz3bt3C/VoNdaqVatp06aSFAMAAKxI6UhUpEiRvHnz6u7LodeSJUt0H/Im1RSRoHjx4r6+vvHx8WI6T58+XXebWFYRAQDgGJSORKrMiaKzZ8+K6Zmenq7V0qhRo3r16klYTKVKlU6dOiWmZ1JSklZLuXLlwsPDJSwGAABYixUiUYUKFURGIl0SThFlCQoKEhmJdI0aNcq8HWctd+PGDTGXID08PBITE9mJ1gw+Pj5SXZ91APny5bN2CQAgO+vMEpn3xurVq7ds2VLaYkxaTpRd4cKFe/XqJW0x4l26dElMN+HTkYfMU79+/QsXLli7CgCAcqwzS2TeG+W4t8vsSDRkyBCzd5y1XLt27e7cuSP8zj5//vyFTFeuXElJSdHq9vbbb1ulPAAA7I7dzBKVK1euQ4cOkhdjXiTKmzfvoEGDJC/GJCUyaabNxo4dO2vWLK0+RCIAAESym1miMWPGyLFw56233nJ3d9edXzGsb9++fn5+khdjifPnz+s2Vq1aVflKAACwR1aIRCbdh5+lWLFiPXv2lKMYIWZVrFhRdw81A9zc3EaMGCFHMZbQG4mYJQIAQCQrRCKVKffhZxEiiLu7u0zFBAUFmRSJunTpUrJkSZmKMc/Tp08fPnyo1VioUCEhfVqlHgAA7I4dRCI/P7/+/fvLV4xJy4mcnJwk2XFWWkwRAQBgIetEIpOWEw0aNChv3rzyFWNSJGrdurUNPq6GhUQAAFjIarNEInt6eXkNGzZM1mJMikS2uckrs0QAAFjI1meJevfuXbBgQVmLCQwMdHZ21t2/TFfdunUbNmwoazHmIRIBAGAhm54lcnV1HT16tNzFeHh4lClT5saNG0Z72uYUkVqtjoqK0mp0cXGxwQt8AADYLOtEoqJFi4q5D79Lly6lS5dWoJ6goCCjkSgwMLB9+/YKFGOqmJgY3S1phdBpxYdrAwBgd6wTiVSZT6M+d+6cgQ5OTk6KzcoIkWj37t2G+9jgjWZZuGoGAIDlrBaJKlSoYDgStWvXLjg4WJlijK6wLl68+Mcff6xMMaYiEgEAYDmrRSKjy4kmTJigTCUqEZFo2LBhbm5uyhRjKr0bthOJAAAwiTVniQwcfeedd+rUqaNYMYYjUb58+WR9VqSFeCgRAACWs9FZIiWniFSZoado0aK6e2Jk6devn4+Pj5L1iJeYmBgbG6vV6OvrW6ZMGStUAwCA3bLFWaIaNWq89957Shajypwo0huJPDw8hg8frnAx4l24cEGtVms1VqlSxSrFAABgv6wWiYoWLZonT55Xr17pHho/frzy9QiR6NChQ7rtH3/8sVCq8vWIxEIiAAAkYbVIpMq8dqZ705nQ+J///Ef5YvQuJ3J2dlbgWZGWYCERAACSsLlINHbsWCcnJ+WL0RuJ2rdvX7FiReWLEc+MO/DfvHnj4+OTlpZm+MzVq1c/c+aMRcUBAGA/rBmJdJcTFStW7JNPPrFKMXojkZDPlK/EJGZcOIuOjk5PTzd65gYNGphfFgAA9sbKs0RaLSNHjnR3d7dKMUIa8/X1jY+P17Q0atRIyQcBmOH27dsvX77UagwICDB8f5wQmB48eLBv374//vhj//79wteaQ66uru3atWueqVy5crIUDQCATbKhWSI/P79+/fpZqxhV5kTRyZMnNS/tdIpIzEKiwoULd+vWrWvXrr169Vq9enVWo5ub24YNGz744ANpiwQAwC5YMxKFhYVlZGRYsQAtx48ft3YJprFkKw+1Wt2jR481a9ZkvXR3d9+8eXPbtm2lrA8AAPthzUgEC5kdiYQkKuShX375Jeulp6fn1q1bW7ZsKXF9AADYDyKRHTMvEgl56JNPPlm7dm3WSy8vr+3bt7/77rvS1wcAgP0gEtmrlJSUmJgYrUYPDw/DTw0Q8tDHH3+8bt26rJd58uTZuXNn48aNZSoSAAB7QSSyV1FRUbrPFgoODnZ2ds7pLUIe6t69+/r167Ne5s2bd8+ePQ0bNpSxSgAA7ASRyF6ZetUsPT1dyEMbNmzIeunr6/vbb7/Vq1dPrvoAALArRCJ7ZVIkEvJQt27dNm7cmPXSz8/v999/DwkJkbE+AADsCpHIXol/KJGQh7p27bpp06asl/7+/vv27atRo4a89QEAYFeIRPZK5CyRkIe6dOmyefPmrJcFCxbcv3+/yGcXAQCQexCJ7FJcXNyjR4+0Ggtnyt4i5KFOnTpt3bpV0+HAgQOVK1dWqEoAAOwHkcgunTt3TrdRa+4nLS2tc+fOmjxUrFgxIQ9VqlRJifoAALA3RCK7ZHQhkZCHOnbsuG3bNk1L//79yUMAAOSESGSXDC8kEvJQhw4dtm/fnv3osmXLxo8f7+bmpkR9AADYGyKRXTIQiVJTU4U8tGPHDq2j9+/fX7VqVZ8+fZSoDwAAe0Mksj8ZGRlRUVFajS4uLsHBwUIe+s9//rNz5069b/zuu+969+7t5OQkf40AANgZIpH9iYmJSU5O1mqsUKGCs7NzeHj4rl27DLxxy5YtQmaSuUAAAOwPkcj+6L1qVqlSpY8++mj37t1ZL999990CBQpotu/QmDFjBpEIgKzi4+NjY2Nv3bql+d+HDx++zpSUlJT1xZs3b9zc3DwyeXp6FixYMOsxIsWLF69YsaLwAy0wMNDf39/aHwW5C5HI/uiNREIYSk1Nzfo6PDx87dq1165d27hxo1qtzt4tMjJy//79QmBSolAAucPNmzfPZnPnzh0x73qTKetrvW8pW7Zsg0zCj6xy5cpJWTGgD5HI/uiNRJo81KdPn4iICGdn56CgoDZt2uheR5s+fTqRCIAl4uPjT506dfz48ROZnj9/LscoNzOtWbNG+LpatWrCH3vdunUTcpIcYwEqIpE90huJsowdO1ZIPJqXY8aM0Y1EBw8e/Oeff2rXri1XfQAcWtWqVS9fvpyRkaHkoOcyTZkypV27dsOGDWvcuLGSoyOXIBLZmYSEhFu3buk9NGPGDCEDZW8JCwurU6fOyZMndXtqdoEFAJNcunTJWkMLOWx7pqZNm86ZM4ftGiEtIpGd0fvcahcXl4iIiN69e+seEkKS7nrqX3/9NSYmpkKFCrKUCAAyO3jwYM2aNQcOHPjdd995eHhYuxw4CCKRndF71axnz55685Dgww8/FKKPEICyNwp/ac2cOfOHH36QpUQAyKZs2bKhoaHVqlWrVKlS6dKlS5YsmSdPHm9v79TU1KSkpPj4+Lt3796+ffvs2bORkZFHjx7VrLk2TPg5tmjRoj///HP9+vVBQUFyfwrkBkQiO6M3EtWoUSOn/k5OTqNGjerfv79W+88//zx16tRixYpJXB8AqFSenp7Nmzdv37698L+lSpXS28c9U758+YQO9erV69Spk9D4+vXrvXv3Llu2bP/+/Vo3zOp14cKFunXr7tix45133pH4MyD3IRLZGb0XzgxfUO/Ro8ekSZMeP36cvTElJWXOnDnfffedxPUByN2qV6/er1+/Ll26+Pr6mvF2b2/vjzKdPXt2xIgRf/75p9G3JCQktGrVauPGjW3btjVjRECDSGRnzIhEHh4eQ4YM+eKLL7Tav//++88//9zPz0/C8gDkWmFhYZMnT27atKkkZxOi1aFDh2bPnj1hwoS0tDTDnZOTkzt27Hjw4MG6detKMjpyJyKRPbl161Z8fLxWY+nSpY3+NTZw4MDp06e/evUqe6Pwp9XixYuFVCRxlQBynw8//HDLli2Sn3bUqFGBgYH/+c9/UlJSDPcUUlH79u1PnToVEBAgeRnIJYhE9kTvQiIxt6Hmz5+/d+/eCxYs0GoXWoSfOJ6entLUByC3ql+/vkxnbtu27cqVK7t27Wq055MnT3r06HH48GGZKoHDIxLZEzOummmMGDFiyZIlWvPPwk+Q5cuXDxo0SJr6AORWoaGh8p28c+fOR48eXbp0qdGeR44cWbRo0eDBg+UrBg6MSGRPzJ4lEgQEBHTo0GHdunVa7bNnz+7fv7+Li4sE9QHIlZydnWvWrCnrENOnT9+2bduDBw+M9pw0adInn3xi3uJu5HJEInuiNxJVrVpV5NvHjBmjG4liY2PXr1/frVs3S4sDkFsFBQXlyZNH1iF8fHymTJnSr18/oz1fvHgxd+7cyZMny1oPHBKRyG68efNG64mLqsy7yQIDA0WeoXr16u++++7+/fu12mfOnEkkAmC2kJAQBUbJep7Io0ePjPacP3/++PHjeao1TEUkshtRUVHp6elajcHBwc7OzuJPMnbsWN1IdOHChd27d7dp08bSEgHkSrIuJNJwd3fv3r377NmzjfZ88eLFzp07dfcyAgwjEtkNSxYSabz77rvVq1c/e/asVvv06dOJRADMo8wskaBLly5iIpEq8wH9RCKYikhkNySJRKrMFUW6l8n+/vvvMmXKNMwUFhZWuXJlM6sEkMu4u7srtiN9zZo1CxQo8PTpU6M9Dx48mJaW5urK7ziYgH8udkOqSNSxY8f//ve/t27d0mq/ffv22kzC18eOHeMhsADEqFatmpubm2LDCX+zbdu2zWi3V69eRUZG1qlTR/6K4DiIRHbDkocSZefi4jJixIjhw4fn1MHJyUn8XWwAcjllFhJpCAlMTCRSZU5+E4lgEiKR3Xj48KFUpxqaSaqzAcjNFFtIlCU4OFhkz+joaFkrgeMhEgEAzKdwJCpVqpTInjdu3JC1EjgeIhEAwAQZGRlWHL1o0aIie8bGxspZCBwQkQgAYDf8/f1F9kxISJC1EjgeIhEAwG6Ifyb1q1evZK0EjodIBACwG+IjUVJSkqyVwPEQiQAAdiM1NVVkT3d3d1krgeMhEgEA7EZKSorInl5eXrJWAsdDJAIA2A3xs0Te3t6yVgLHQyQCANiN+Ph4kT3F364PZCESAQDsxrNnz0T2LFGihKyVwPEQiQAAduPp06cie4p/zjWQhUgEALAbjx8/FtmzSpUqslYCx0MkAgDYjZs3b4rs+fbbb8taCRwPkQgAYDdE7lzm6upKJIKpiEQAALsRExMjpludOnXy5MkjdzFwMEQiAIDdOHfunJhuzZo1k7sSOB4iEQDAPsTGxr548UJMz3bt2slcCxwQkQgAYB9OnTolplv58uVr1aoldzFwPEQiAIB9OHjwoJhuXbp0kbsSOCQiEQDAPhw6dMhoHxcXlz59+ihQDBwPkQgAYAdiMhnt1rZtW55bDfMQiQAAdmDz5s1iuo0YMULuSuCoiEQAADuwadMmo30aZVKgGDgkIhEAwNZFRkaePXvWaLcpU6bIXgocF5EIAGDrli1bZrRP27ZtGzduLH8tcFhEIgCATXv69OnatWsN93Fzc5s9e7Yy9cBREYkAADZt7ty5r1+/Ntxn1KhRFSpUUKYeOCoiEQDAdr148WLx4sWG+wQGBk6ePFmZeuDAiEQAANs1derUly9fGujg4uKyYsUKDw8PxUqCoyISAQBs1LVr14xOEU2cOLFevXrK1APHRiQCANioQYMGpaamGugQFhb2xRdfKFYPHBuRCABgi1avXr1v3z4DHYoVK7Z+/XpnZ2fFSoJjIxIBAGzO/fv3R44caaCDu7v7li1bhFSkWElweEQiAIBtUavV3bt3f/bsmYE+S5curVu3rmIlITcgEgEAbMu0adMOHz5soMOkSZN69eqlVDnILYhEAAAb8ttvvxneqkwIQ+xlBjkQiQAAtuLq1atdu3bNyMjIqUN4ePgPP/ygZEnIPYhEAACb8OTJkzZt2hh4MGOrVq3Wrl3LLWaQCZEIAGB9SUlJbdu2vX79ek4dmjVrtmXLFjc3NyWrQq5CJAIAWFlaWlqHDh1Onz6dU4emTZvu3LnT09NTyaqQ2xCJAADWpFarP/nkkz179uTUgTwEZRCJAADWNHDgwPXr1+d0tGXLllu3biUPQQFEIgCA1QwbNmzZsmU5Hf3ggw82bNjA+iEog0gEALCO0aNHL1y4MKej3bt3/+mnn1xcXJQsCbkZkQgAYAUjR46cN29eTkeHDh1q4CggByIRAEBpgwcPXrJkSU5Hp06dOnHiRCXrAVREIgCAktRqdd++fVesWKH3qIuLy9KlS/v06aNwVYCKSAQAUExaWlr37t03btyo96inp+f69evff/99hasCshCJAABKSE5ODg8P/+233/Qe9ff337FjR/369RWuCtAgEgEAZPfy5cu2bdv+/fffeo+WKVNGiEqBgYEKVwVkRyQCAMjr4cOHLVq0uHDhgt6jNWrU2LNnT5EiRRSuCtBCJAIAyOj69evvvffezZs39R5t1arVxo0b8+TJo3BVgC4iEQBALpGRka1bt37y5Ineo3379l2yZAkPY4SNIBIBAGSxb9++8PDwxMRE3UNOTk5ff/31hAkTlK8KyAmRCAAgvTVr1vTu3Ts1NVX3kIeHx8qVKzt16qR8VYABRCIAgMS+/fbbzz//XO+hAgUKbN++nZvtYYOIRAAAyWRkZAwePDgiIkLv0QoVKuzZs6dcuXIKVwWIQSQCAEgjOTm5c+fOO3bs0Hu0YcOG27Zt8/f3V7gqQCQiEQBAAk+fPm3Xrt2JEyf0HhWi0sqVK93d3RWuChCPSAQAsNTNmzdbtmwZExOj9+i4ceO+/fZbhUsCTEUkAgBY5OzZs61atXr06JHuIRcXl4ULF/bv31/5qgBTEYkAAOY7cODARx99lJCQoHvI29t7/fr1bdu2Vb4qwAxEIgCAmTZs2NCjR4+UlBTdQ4UKFdq1a1dISIjyVQHmIRIBAMyxcOHC4cOHq9Vq3UPlypXbu3cvN9vDvhCJAAAmmzhx4jfffKP3UK1atfbs2VOoUCGFSwIsRCQCAJggIyOjX79+y5cv13u0RYsWmzdvZmd72CMiEQBArJSUlC5duvz66696j3br1u2nn35ydeU3C+wS/3ABAKIkJia2b9/+0KFDeo+OHDly1qxZCpcESIhIBAAwLi4urlWrVpGRkXqPzpgxY8yYMQqXBEiLSAQAMC4sLCw6Ojqno+MyKVmPeBkZGdYuAfaBSAQAMM5AHgIcA5EIAACASAQAAEAkAgAAUBGJAAAAVEQiAAAAFZEIAABARSQCAABQEYkAAABURCIAAAAVkQgAAEBFJAIAiMFOYXB4RCIAAAAiEQAAAJEIAABARSQCAABQEYkAAABURCIAAAAVkQgAAEBFJAIAAFARiQAAAFREIgAAABWRCAAAQEUkAgAAUBGJAAAAVEQiAAAAFZEIAABARSQCAABQEYkAAABURCIAAAAVkQgAAEBFJAIAAFARiQAAAFREIgAAABWRCAAAQEUkAgAAUBGJAAAAVEQiAAAAFZEIAABARSQCAABQEYkAAABURCIAAAAVkQgAAEBFJAIAAFARiQAAAAT/D31Qe7bk/MVLAAAAAElFTkSuQmCC)
Үйкеліс күші жоқ болғанда энергияның сақталу заңы бойынша, потенциалдық энергияның ең үлкен мәні кинетикалық энергияның ең үлкен мәніне тең болады:
mgHe.y. .
6- сурет
Маятник тербелген кезде потенциалдық энергияның кинетикалық энергияға және керісінше түрленуі периодты түрде қайталанып отырады:
Wp → Wk → Wp → Wk → Wp → … .
Энергияның айналу және сақталу заңы бойынша тербеліп тұрған дененің толық механикалық энергиясы потенциалдық және кинетикалық энергиялардың қосындысына тең болады:
E= Wp + Wk.
Маятникті тепе-теңдік қалпынан ауытқытып жіберіп, оның еркін тербелістер жасауына мүмкіндік береміз. Тербеліс амплитудасының бірте-бірте азая беретінін байқауға болады. Олай болатын себебі, алғашқы кездегі маятникке берілген энергия ішкі энергияға айналады да, қоршаған ортаға таралып кетеді. Егер үйкеліс болмаса, онда тербелмелі жүйенің энергиясы тұрақты болып қалар еді де, тербеліс шексіз болар еді.
Достарыңызбен бөлісу: |