Question

A linear harmonic oscillator of force constant $2\times 10^6$ $N{m}^{-1}$ and amplitude $0.01m$ has a total mechanical energy $160J$. Among the following statements, which are correct?
i. Maximum PE is $100J$
ii. Maximum $KE$ is $100J$
iii. Maximum $PE$ is $160J$
iv. Minimum $PE$ is zero

• A. Both (i) and (iv)
• B. Both (ii) and (iii)
• C. Both (i) and (ii)
• D. Both (ii) and (iv)

Answer 1

Answer: (B)

Total mechanical energy is $E_T=160J$
$\therefore U_{\max }=160J$
At extreme position $KE$ is zero. Work done by spring force from extreme position to mean position is $W=\frac{1}{2}k{A}^2$
$\therefore K_{\max }=W=\frac{1}{2}\left(2\times 10^6\right)(0.01{)}^2=100J$
$\therefore U_{\min }=160-100=60J$