MCQ
A body is executing simple harmonic motion with frequency $'n',$ the frequency of its potential energy is :
- A$\mathrm{n}$
- B$3 \mathrm{n}$
- ✓$2 \mathrm{n}$
- D$4 \mathrm{n}$
✓
Answer
Correct option: C.
$2 \mathrm{n}$
c
Displacement equation of $SHM$ of frequency $'n'$
Displacement equation of $SHM$ of frequency $'n'$
$\mathrm{x}=\mathrm{A} \sin (\omega \mathrm{t})=\mathrm{A} \sin (2 \pi \mathrm{nt})$
Now,
Potential energy
$U=\frac{1}{2} k x^{2}=\frac{1}{2} K A^{2} \,\sin ^{2}(2 \pi n t)$
$=\frac{1}{2} k A^{2}\left[\frac{1-\cos (2 \pi(2 n) t)}{2}\right]$
So frequency of potential energy $=2 \mathrm{n}$
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