(C) The given equation of motion is $\frac{d^2y}{dt^2} + Ky = 0$.Comparing this with the standard equation of Simple Harmonic Motion $(SHM)$,which is

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(C) The given equation of motion is $\frac{d^2y}{dt^2} + Ky = 0$.Comparing this with the standard equation of Simple Harmonic Motion $(SHM)$,which is $\frac{d^2y}{dt^2} + \omega^2 y = 0$,we get $\omega^2 = K$.Therefore,the angular frequency is $\omega = \sqrt{K}$.We know that the time period $T$ is related to the angular frequency $\omega$ by the formula $T = \frac{2\pi}{\omega}$.Substituting the value of $\omega$,we get $T = \frac{2\pi}{\sqrt{K}}$.

Class 11 Physics Oscillations Periodic, Oscillatory motion and its characteristics and types of SHM and Equation of SHM

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The equation of motion of a particle is $\frac{d^2y}{dt^2} + Ky = 0$,where $K$ is a positive constant. The time period of the motion is given by

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

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The equation of motion of a particle is $\frac{d^2y}{dt^2} + Ky = 0$,where $K$ is a positive constant. The time period of the motion is given by

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