A) \[f\]
B) \[2f\]
C) \[f/2\]
D) \[4f\]
Correct Answer: B
Solution :
\[y=a\,\sin \,\omega \,t\] \[=a\,\sin \,2\pi f\,t\] \[(\therefore \omega =2\pi f)\] \[\therefore \]Kinetic energy \[=\frac{1}{2}m{{\left( \frac{dy}{dt} \right)}^{2}}\] \[=\frac{1}{2}m\left( {{(2\pi fa)}^{2}}\,\cos {{\,}^{2}}2\pi ft \right)\] \[\propto \cos {{\,}^{2}}2\pi ft\propto (1+\cos 4\pi ft)\] \[\cos \,(4\pi ft)\]changes periodically by frequency of \[2f.\]
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