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(B) The general equation for $Simple \ Harmonic \ Motion$ is given by $x = A \cos(nt + \phi)$,where $A$ is the amplitude and $\phi$ is the phase const

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$\frac{d^2x}{dt^2} + n^2x = 0$

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(B) The general equation for $Simple \ Harmonic \ Motion$ is given by $x = A \cos(nt + \phi)$,where $A$ is the amplitude and $\phi$ is the phase constant.First,differentiate $x$ with respect to $t$:$\frac{dx}{dt} = -An \sin(nt + \phi)$Next,differentiate again with respect to $t$ to find the second derivative:$\frac{d^2x}{dt^2} = -An^2 \cos(nt + \phi)$Since $x = A \cos(nt + \phi)$,we can substitute this into the equation:$\frac{d^2x}{dt^2} = -n^2 x$Rearranging the terms gives the differential equation:$\frac{d^2x}{dt^2} + n^2x = 0$.

The differential equation of displacement of all $Simple \ Harmonic \ Motions$ of given period $T = 2\pi / n$ is:

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