A simple harmonic oscillator of angular frequency 2rad s ^ - 1 is acted upon by an external force F = sin tN . If the oscillator is at rest in its equilibrium position at t = 0, its position at later times is

Question

Quantrex Academy · Accepted Answer

Correct answer: C. sin t - (1)/(2) 2t

It is given that oscillator at rest at t = 0 i.e. at t = 0 , v = 0 . So, in option, we can check by putting v = (dx)/(dt) = 0 . (1) Ifx ∝ sin t + (1)/(2) 2t ⟹ v ∝ cos t + (1)/(2) × 2 ( - 2t ) ⟹ att = 0, v ∝ 1 - 0 ≠ 0 (2) Ifx ∝ cos t - (1)/(2)sin t ⟹ v ∝ - sin t - (1)/(2)cos t ⟹ att = 0, v ∝ - (1)/(2) ≠ 0 (3) Ifx ∝ sin t - (1)/(2) 2t thenυ ∝ cos t - (1)/(2) × 2 2t ⟹ att = 0, v ∝ 1 - 1 = 0 (4) Ifx ∝ sin t + (1)/(2) 2t ⟹ v ∝ cos t + (1)/(2) × 2 2t ⟹ att = 0, v ∝ 1 + 1 ⟹ v ∝ 2 ≠ 0 ∴ inoption(3)v = 0att = 0

A simple harmonic oscillator of angular frequency 2rad s ^ - 1 is...

Options

Correct answer

Step-by-step solution

More from Oscillations