(A) The standard equation for Simple Harmonic Motion $(SHM)$ is given by $\frac{d^2x}{dt^2} + \omega^2x = 0$.Comparing the given equation $\frac{d^2x}

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(A) The standard equation for Simple Harmonic Motion $(SHM)$ is given by $\frac{d^2x}{dt^2} + \omega^2x = 0$.Comparing the given equation $\frac{d^2x}{dt^2} + \pi^2x = 0$ with the standard equation,we get $\omega^2 = \pi^2$.Taking the square root,we find $\omega = \pi \, rad/s$.The relationship between angular frequency $\omega$ and frequency $f$ is given by $\omega = 2\pi f$.Therefore,$f = \frac{\omega}{2\pi} = \frac{\pi}{2\pi} = 0.5 \, Hz$.

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 of mass $1\,g$ is $\frac{d^2x}{dt^2} + \pi^2x = 0$,where $x$ is displacement (in $m$) from the mean position. The frequency of oscillation is (in $Hz$):

A
$0.5$
B
$2$
C
$5\sqrt{10}$
D
$\frac{1}{5\sqrt{10}}$

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Oscillations

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Periodic, Oscillatory motion and its characteristics and types of SHM and Equation of SHM

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Equations $y_1 = A \sin \omega t$ and $y_2 = \frac{A}{2} \sin \omega t + \frac{A}{2} \cos \omega t$ represent $S.H.M.$ The ratio of the amplitudes of the two motions is

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The equation of motion of a particle of mass $1\,g$ is $\frac{d^2x}{dt^2} + \pi^2x = 0$,where $x$ is displacement (in $m$) from the mean position. The frequency of oscillation is (in $Hz$):

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