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<title>Measurements of the circular frequency of oscillations of a body of mass m, fixed in the middle of a tensioned string with length 2 l, gave the value \omega. Find the force of tension of the string.</title>
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<title>Measurements of the circular frequency of oscillations of a body of mass m, fixed in the middle of a tensioned string with length 2 l, gave the value \omega . Find the force of tension of the string.</title>
$3.2.10.$ Measurements of the circular frequency of oscillations of a body of mass $m$, fixed in the middle of a tensioned string with length $2 l$, gave the value $\omega$. Find the force of tension of the string.
</p>
<h3>Solution</h3>
<p>
The total external force acting on the system
$$ F=2T\sin\varphi$$
Newton's second law
$$ m\ddot{x}(t)+2T\sin\varphi=0 $$
Let's use the approximation for small angles $(\varphi\ll 1)$:
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<meta name="description" content="Measurements of the circular frequency of oscillations of a body of mass m, fixed in the middle of a tensioned string with length 2 l, gave the value \omega. Find the force of tension of the string.">
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<meta property="og:description" content="Measurements of the circular frequency of oscillations of a body of mass m, fixed in the middle of a tensioned string with length 2 l, gave the value \omega. Find the force of tension of the string.">
<meta property="og:description" content="Measurements of the circular frequency of oscillations of a body of mass m, fixed in the middle of a tensioned string with length 2 l, gave the value \omega. Find the force of tension of the string.">
<title>Measurements of the circular frequency of oscillations of a body of mass m, fixed in the middle of a tensioned string with length 2 l, gave the value \omega. Find the force of tension of the string.</title>
<title>Measurements of the circular frequency of oscillations of a body of mass m, fixed in the middle of a tensioned string with length 2 l, gave the value \omega . Find the force of tension of the string.</title>
$3.2.10.$ Measurements of the circular frequency of oscillations of a body of mass $m$, fixed in the middle of a tensioned string with length $2 l$, gave the value $\omega$. Find the force of tension of the string.
$3.2.10.$ Measurements of the circular frequency of oscillations of a body of mass $m$, fixed in the middle of a tensioned string with length $2 l$, gave the value $\omega$. Find the force of tension of the string.
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
The total external force acting on the system
The total external force acting on the system
$$ F=2T\sin\varphi$$
$$ F=2T\sin\varphi$$
Newton's second law
Newton's second law
$$ m\ddot{x}(t)+2T\sin\varphi=0 $$
$$ m\ddot{x}(t)+2T\sin\varphi=0 $$
Let's use the approximation for small angles $(\varphi\ll 1)$:
Let's use the approximation for small angles $(\varphi\ll 1)$:
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
