Question

A linear harmonic oscillator of force constant $2\times 10^{6}N/m$ times and amplitude $0.01m$ has a total mechanical energy of $160$ joules. Its

• A. Maximum potential energy is $100J$
• B. Maximum K.E. is $160J$
• C. Maximum P.E. is $160J$
• D. Minimum P.E. is zero

Answer 1

Answer: (C)

Harmonic oscillator has some initial elastic potential energy and amplitude of harmonic variation of energy is
$\frac{1}{2}k{a}^2=\frac{1}{2}\times 2\times 10^6(0.01{)}^2=100J$
This is the maximum kinetic energy of the oscillator.
Thus, $K_{\max }=100J$
This energy is added to initial elastic potential energy may give maximum mechanical energy to have value $160J$.