(B) In $SHM$,the kinetic energy $K(x)$ and potential energy $U(x)$ are given by:$K(x) = \frac{1}{2}m\omega^2(A^2 - x^2)$$U(x) = \frac{1}{2}m\omega^2x^

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(B) In $SHM$,the kinetic energy $K(x)$ and potential energy $U(x)$ are given by:$K(x) = \frac{1}{2}m\omega^2(A^2 - x^2)$$U(x) = \frac{1}{2}m\omega^2x^2$At the point $x = x_0$,the kinetic energy and potential energy are equal,i.e.,$K(x_0) = U(x_0)$.$\frac{1}{2}m\omega^2(A^2 - x_0^2) = \frac{1}{2}m\omega^2x_0^2$$A^2 - x_0^2 = x_0^2$$A^2 = 2x_0^2$$x_0^2 = \frac{A^2}{2}$$|x_0| = \frac{A}{\sqrt{2}}$

Class 11 Physics Oscillations Energy of Simple Harmonic Motion

Medium

The variations of kinetic energy $K(x)$,potential energy $U(x)$,and total energy $E$ as a function of displacement $x$ of a particle in $SHM$ are as shown in the figure. The value of $|x_0|$ is

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A
$2A$
B
$\frac{A}{\sqrt{2}}$
C
$\sqrt{2}A$
D
$\frac{A}{2}$

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Class 11

Physics Questions

Chapter

Oscillations

Subtopic

Energy of Simple Harmonic Motion

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$A$ body performs linear simple harmonic motion of amplitude $A$. At what displacement from the mean position is the potential energy of the body one-fourth of its total energy?

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If $T$ is the period of $SHM$,then write the period of kinetic and potential energy.

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$A$ body is performing $SHO$ with a total energy of $100\,J$. In the table below, column-$I$ shows the kinetic energy $(K)$ at a specific time, and column-$II$ shows the potential energy $(U)$ at that same time. Match them appropriately.
Column-$I$ Column-$II$
$(a)$ $K = 10\,J$ $(i)$ $U = 40\,J$
$(b)$ $K = 60\,J$ $(ii)$ $U = 90\,J$
$(iii)$ $U = 50\,J$

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$A$ particle oscillates along the $x$-axis according to the law,$x(t) = x_0 \sin^2\left(\frac{t}{2}\right)$,where $x_0 = 1 \text{ m}$. The kinetic energy $(K)$ of the particle as a function of $x$ is correctly represented by the graph.

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$A$ linear harmonic oscillator of force constant $6 \times 10^5 \, N/m$ and amplitude $4 \, cm$ has a total energy of $600 \, J$. Select the correct statement.

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Column-$I$	Column-$II$
$(a)$ $K = 10\,J$	$(i)$ $U = 40\,J$
$(b)$ $K = 60\,J$	$(ii)$ $U = 90\,J$
	$(iii)$ $U = 50\,J$

The variations of kinetic energy $K(x)$,potential energy $U(x)$,and total energy $E$ as a function of displacement $x$ of a particle in $SHM$ are as shown in the figure. The value of $|x_0|$ is

Similar Questions

$A$ body performs linear simple harmonic motion of amplitude $A$. At what displacement from the mean position is the potential energy of the body one-fourth of its total energy?

If $T$ is the period of $SHM$,then write the period of kinetic and potential energy.

$A$ particle oscillates along the $x$-axis according to the law,$x(t) = x_0 \sin^2\left(\frac{t}{2}\right)$,where $x_0 = 1 \text{ m}$. The kinetic energy $(K)$ of the particle as a function of $x$ is correctly represented by the graph.

$A$ linear harmonic oscillator of force constant $6 \times 10^5 \, N/m$ and amplitude $4 \, cm$ has a total energy of $600 \, J$. Select the correct statement.

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