Question

A particle with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force Fsinωt. If the amplitude of the particle is maximum for ω=ω1 and the energy of the particle maximum for ω=ω2, then?

(a) ω1≠ω0  and ω2=ω0

(b) ω1=ω0  and ω2=ω0

(c) ω1≠ω0  and ω2≠ω0

(d) ω1≠ω0  and ω2≠ω0

The question was posed to me in exam.

This intriguing question originated from Wave Motion topic in division Waves of Engineering Physics I

Answer 1

The correct choice is (a) ω1≠ω0  and ω2=ω0

The explanation is: In a driven harmonic oscillator, the energy is maximum at ω2=ω0 and amplitude is maximum at frequency, ω1 is lesser than ω0 in the presence of a damping of force. Therefore, ω1≠ω0  and ω2=ω0.