JEE Mains · Physics · STD 11 - Oscillations
- JEE Mains 2015
- Hard
- MCQ
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
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(\sin \,t\, - \,\frac{1}{2}\,\sin \,2t\)
Step-by-step Solution
Detailed explanation
As we know,
\(F=m a \Rightarrow a \propto F\)
or, \(a \propto \sin t\)
\(\Rightarrow \frac{d v}{d t} \propto \sin t\)
\(\Rightarrow \int_{0}^{0} d V \propto \int_{0}^{t} \sin t d t\)
\(V \propto-\cos t+1\)
\(\int_{0}^{x} d x=\int_{0}^{t}(-\cos t+1) d t\)
\(x=\sin t-\frac{1}{2} \sin 2 t\)
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