Question

A particle of mass $0.3\text{kg}$ executes SHM with an amplitude $0.06\text{m}$ and frequency $10$ vibrations/sec. Find its total energy of oscillation.

• A. $5\text{J}$
• B. $2.13\text{J}$
• C. $3\text{J}$
• D. $8.5\text{J}$

Answer 1

The correct option is B $2.13\text{J}$

Given, mass $\left(m\right)=0.3\text{kg}$
Amplitude $\left(A\right)=0.06\text{m}$
frequency $\left(f\right)=10\text{Hz}$
We know that $T=\frac{2\pi }{\omega }$
and $f=\frac{1}{T}=\frac{\omega }{2\pi }$
$\Rightarrow \omega =2\pi f$
Energy of oscillation $\left(E\right)=\frac{1}{2}m{\omega }^2{A}^2=\frac{1}{2}m(2\pi f{)}^2{A}^2$
$=2{\pi }^2{f}^{2}m{A}^2$
$=2\times (3.14{)}^2\times (10{)}^2\times 0.3\times (0.06{)}^2=2.13\text{J}$