(A) For a simple harmonic oscillator,the potential energy $V$ at displacement $x$ is given by $V = \frac{1}{2} k x^2$,where $k = m \omega^2$.The kinet

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(A) For a simple harmonic oscillator,the potential energy $V$ at displacement $x$ is given by $V = \frac{1}{2} k x^2$,where $k = m \omega^2$.The kinetic energy $T$ at displacement $x$ is given by $T = \frac{1}{2} k (A^2 - x^2)$.Taking the ratio $\frac{V}{T}$:$\frac{V}{T} = \frac{\frac{1}{2} k x^2}{\frac{1}{2} k (A^2 - x^2)}$$\frac{V}{T} = \frac{x^2}{A^2 - x^2}$

Class 11 Physics Oscillations SHM of Simple Pendulum

Medium

The angular velocity and the amplitude of a simple pendulum are $\omega$ and $A$ respectively. At a displacement $x$ from the mean position,its kinetic energy is $T$ and potential energy is $V$. Then the ratio $\frac{V}{T}$ is

A
$\frac{x^2}{A^2 - x^2}$
B
$\frac{A^2 - x^2}{x^2}$
C
$\frac{x^2 \omega^2}{A^2 - x^2}$
D
$\frac{A^2 - x^2}{x^2 \omega^2}$

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SHM of Simple Pendulum

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$A$ cylindrical cork of uniform density floats in a liquid of density $\rho_1$. If the cork is depressed slightly and released, it oscillates harmonically with time period $T$. If the same cork floats in another liquid of density $\rho_2$, then the similar oscillation has time period $2T$. The value of $\rho_2/\rho_1$ is :

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The angular velocity and the amplitude of a simple pendulum are $\omega$ and $A$ respectively. At a displacement $x$ from the mean position,its kinetic energy is $T$ and potential energy is $V$. Then the ratio $\frac{V}{T}$ is

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An oscillating pendulum suspended from the roof of a lift which is at rest has time period $T_1$. When the lift moves up with acceleration $a$, its time period is $T_2$. When the lift moves down with acceleration $a$, its time period is $T_3$. The relation between $T_1$, $T_2$, and $T_3$ is:

The bob of a simple pendulum of length $L$ is released from a position of small angular displacement $\theta$. Its linear displacement at time $t$ is ($g =$ acceleration due to gravity).

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$A$ simple pendulum with a bob of mass $m$ oscillates from $A$ to $C$ and back to $A$ such that $PB$ is $H$. If the acceleration due to gravity is $g$,then the velocity of the bob as it passes through $B$ is

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