A) periodic but not SHM
B) non periodic
C) simple harmonic motion with period 0.1 s
D) simple harmonic motion with period 0.2 s
Correct Answer: C
Solution :
The standard equation of SHM wave of amplitude a, angular frequency co, and phase is \[y=a\,\sin (\omega \,t+\phi )\] ... (i) where t is time. Given equation is \[y=0.2\,\sin \,(10\pi t+5\pi )\,\cos \,(10\pi t+1.5\pi )\] Using the relation \[\sin \,2\theta =2\sin \theta cos\theta \], we have \[y=0.1\,\sin 2\,(10\pi t+1.5\pi )\] \[\Rightarrow \] \[y=0.1\,\sin \,(20\pi t+3\pi )\] ... (ii) On comparing Eqs. (i) and (ii), we get \[\omega =20\pi \], Hence, time period, \[T=\frac{2\pi }{\omega }=\frac{2\pi }{20\pi }\] \[\Rightarrow \] \[T=\frac{1}{10}=0.1\,\,s\]You need to login to perform this action.
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