Wave Mechanics Question 535
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 given by:
Options:
A) $ \sin ,t+\frac{1}{2}\cos ,2t $
B) $ \cos t-\frac{1}{2}\sin ,2t $
C) $ \sin t-\frac{1}{2}\sin ,2t $
D) $ \sin t+\frac{1}{2}\sin ,2t $
Show Answer
Answer:
Correct Answer: C
Solution:
As we know, $ F=ma\Rightarrow a\propto F,,a\propto \sin ,t $ $ \Rightarrow \frac{dv}{dt}\propto \sin t\Rightarrow \int\limits _{0}^{t}{dV\propto \int\limits _{0}^{t}{\sin t,dt}} $
$ V\propto -\cos ,t+1 $
$ \int\limits _{0}^{x}{dx}=\int\limits _{0}^{x}{(-\cos t+1)dt} $
$ x=\sin ,t-\frac{1}{2}\sin 2t $
BETA
