The equation of motion of a particle executin | vedclass

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(D) The given equation of motion is $4 \frac{d^2 y}{dt^2} + \pi^2 y = 0$.Dividing by $4$,we get $\frac{d^2 y}{dt^2} + \frac{\pi^2}{4} y = 0$.The gener

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(D) The given equation of motion is $4 \frac{d^2 y}{dt^2} + \pi^2 y = 0$.Dividing by $4$,we get $\frac{d^2 y}{dt^2} + \frac{\pi^2}{4} y = 0$.The general equation for simple harmonic motion is $\frac{d^2 y}{dt^2} + \omega^2 y = 0$.Comparing the two equations,we find $\omega^2 = \frac{\pi^2}{4}$,which gives $\omega = \frac{\pi}{2} \ rad/s$.The time period $T$ is given by the formula $T = \frac{2\pi}{\omega}$.Substituting the value of $\omega$,we get $T = \frac{2\pi}{\pi/2} = 2\pi 	imes \frac{2}{\pi} = 4 \ s$.

The equation of motion of a particle executing simple harmonic motion is $4 \frac{d^2 y}{dt^2}+\pi^2 y=0$,where $y$ is in metres and $t$ is in seconds. The time period of oscillation of the particle is (in $s$)

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