Translated 3.2.1-3.2.17

astrosander правка от 28 сент. 2024 г., 01:02

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		+	<body style="">
		+	<header style="text-align:center;">
		+	<div id = "logo">
		+	<span><img src = "../../img/book.png"><span><span>Savchenko Solutions</span>
		+	</div>
		+	<p class="author">
		+	Solutions of Savchenko Problems in Physics <br>
		+	<i><b>knowledge must be free</b></i>
		+	</p>
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		+
		+	<h3 id="back-link"><a href="../../#3.2">$\leftarrow$Back</a></h3>
		+
		+	<h3> Statement </h3>
		+	<p>
		+	$3.2.2.$ A fixed weight suspended on a spring stretches it in the equilibrium position by a length $\Delta l$. What is the period of vertical oscillations of the load?
		+	</p>
		+
		+	<h3>Solution</h3>
		+	<p>
		+	Period of oscillation of a spring pendulum
		+	$$ T=2\pi\sqrt{\frac{m}{k}} $$
		+	Elastic force, restoring force:
		+	$$ F=-k\Delta l=mg\Rightarrow k=\frac{mg}{\Delta l} $$
		+	The period of oscillation of a spring pendulum, being in the equilibrium position, is $\Delta l$
		+	$$ \boxed{T=2\pi\sqrt{\frac{m\Delta l}{mg}}=2\pi\sqrt{\frac{\Delta l}{g}}} $$
		+
		+	<p style="text-align: right; font-style: italic; font-size: 14;">
		+	Dzikan Mikita<br>
		+	</p>
		+
		+	<h4>Answer</h4>
		+	<p>
		+	$$T=2\pi\sqrt{\frac{\Delta l}{g}}$$
		+	</p>
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			<meta name="viewport" content="width=device-width, initial-scale=1.0">
			<meta http-equiv="content-language" content="en">
			<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
			<meta name="description" content="A fixed weight suspended on a spring stretches it in the equilibrium position by a length \Delta l. What is the period of vertical oscillations of the load?">
			<meta name="author" content="Aliaksandr Melnichenka">
			<meta name="date" content="2023-10" scheme="YYYY-MM">
			<meta property="og:title" content="A fixed weight suspended on a spring stretches it in the equilibrium position by a length \Delta l. What is the period of vertical oscillations of the load?">
			<meta property="og:image" content="img/logo.png">
			<meta property="og:description" content="A fixed weight suspended on a spring stretches it in the equilibrium position by a length \Delta l. What is the period of vertical oscillations of the load?">
			<meta name="yandex-verification" content="6cfda41f74038368">
			<title>A fixed weight suspended on a spring stretches it in the equilibrium position by a length \Delta l. What is the period of vertical oscillations of the load?</title>
			<link rel="stylesheet" href="https://savchenkosolutions.com/css/css-latex/style.css">
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			messageStyle: 'none'
			});
			</script>
			</head>
			<body style="">
			<header style="text-align:center;">
			<div id = "logo">
			<span><img src = "../../img/book.png"><span><span>Savchenko Solutions</span>
			</div>
			<p class="author">
			Solutions of Savchenko Problems in Physics <br>
			<i><b>knowledge must be free</b></i>
			</p>
			</header>

			<h3 id="back-link"><a href="../../#3.2">$\leftarrow$Back</a></h3>

			<h3> Statement </h3>
			<p>
			$3.2.2.$ A fixed weight suspended on a spring stretches it in the equilibrium position by a length $\Delta l$. What is the period of vertical oscillations of the load?
			</p>

			<h3>Solution</h3>
			<p>
			Period of oscillation of a spring pendulum
			$$ T=2\pi\sqrt{\frac{m}{k}} $$
			Elastic force, restoring force:
			$$ F=-k\Delta l=mg\Rightarrow k=\frac{mg}{\Delta l} $$
			The period of oscillation of a spring pendulum, being in the equilibrium position, is $\Delta l$
			$$ \boxed{T=2\pi\sqrt{\frac{m\Delta l}{mg}}=2\pi\sqrt{\frac{\Delta l}{g}}} $$

			<p style="text-align: right; font-style: italic; font-size: 14;">
			Dzikan Mikita<br>
			</p>

			<h4>Answer</h4>
			<p>
			$$T=2\pi\sqrt{\frac{\Delta l}{g}}$$
			</p>


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