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(B) For a simple harmonic oscillator,the displacement is given by $x(t) = A \sin(\omega t)$.The period of oscillation is $T = 2\,s$,so the angular fre

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Potential energy

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(B) For a simple harmonic oscillator,the displacement is given by $x(t) = A \sin(\omega t)$.The period of oscillation is $T = 2\,s$,so the angular frequency is $\omega = \frac{2\pi}{T} = \pi\,rad/s$.Velocity is $v(t) = A\omega \cos(\omega t)$,which oscillates with the same period $T = 2\,s$.Potential energy is $U = \frac{1}{2} k x^2 = \frac{1}{2} k A^2 \sin^2(\omega t) = \frac{1}{4} k A^2 (1 - \cos(2\omega t))$. This oscillates with a period $T' = \frac{T}{2} = 1\,s$.Kinetic energy is $K = \frac{1}{2} m v^2 = \frac{1}{2} m A^2 \omega^2 \cos^2(\omega t) = \frac{1}{4} m A^2 \omega^2 (1 + \cos(2\omega t))$. This also oscillates with a period $T' = 1\,s$.The difference between kinetic and potential energy is $K - U = \frac{1}{2} m \omega^2 A^2 \cos(2\omega t)$,which oscillates with a period $T' = 1\,s$.However,in standard physics problems of this type,Potential Energy is the classic example of a quantity oscillating at double the frequency (half the period) of the displacement.

$A$ vertical mass-spring system executes simple harmonic oscillations with a period of $2\,s$. $A$ quantity of this system which exhibits simple harmonic variation with a period of $1\,s$ is

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