Question

A linear harmonic oscillator of force constant $2 \times 10^{6}$ $Nm ^{-1}$ and amplitude $0.01 \,m$ has a total mechanical energy $160\, J$. Among the following statements, which are correct?
i. Maximum PE is $100 \,J$
ii. Maximum $KE$ is $100 \,J$
iii. Maximum $PE$ is $160 \,J$
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 $E_{T}=160 \,J$
$\therefore U_{\max }=160\, J$
At extreme position $KE$ is zero. Work done by spring force from extreme position to mean position is $W=\frac{1}{2} k A^{2}$
$\therefore K_{\max }=W=\frac{1}{2}\left(2 \times 10^{6}\right)(0.01)^{2}=100\, J$
$\therefore U_{\min }=160-100=60\,J$