SHMHard
Question
A simple harmonic oscillator of angular frequency 2 rad s-1 is acted upon by an external force F = sin t N. If the oscillator is at rest in its equilibrium position at t = 0, its position at later times is proportional to :
Options
A.cos t − 1/2 sin 2t
B.sin t + 1/2 cot 2t
C.sin t + 1/2 sin 2t
D.sin t − 1/2 sin 2t
Solution
F = ma
a ∝ sin t
∝ sin t
sin t dt
V ∝ - cos t + 1
(- cost + 1)dt
x = - sin t + t
a ∝ sin t
∝ sin t sin t dtV ∝ - cos t + 1
(- cost + 1)dtx = - sin t + t
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