Question

Force acting on a particle is F = –8x in S.H.M. The amplitude of oscillations is 2 (in m) and mass of the particle is 0.5 kg. The total mechanical energy of the particle is 20 J. The potential energy of the particle at mean position (in J) is ___

Answer 1

$k=8N/m,a=\frac{F}{m}=\frac{8x}{0.5}=16x\omega =\sqrt{16}=4rad/sec\frac{1}{2}k{A}^2=\frac{1}{2}\left(8\right)(2{)}^2=16J$
Potential energy at mean position
$=E-\frac{1}{2}k{A}^2=20-16=4J$