Question
If 0-1 kg the dimension of the body is 3 cm and if the oscillation period is 2 seconds, then what will be the value of total mechanical energy?
✓
Answer
Total energy $=\frac{1}{2} m \omega^2 A^2$
$ \begin{aligned} & =\frac{1}{2} m(2 \pi n)^2 A^2 \\ & =\frac{1}{2} m\left(\frac{2 \pi}{T}\right)^2 A^2 \because n=\frac{1}{T} \\ \text { Keeping value } & =\frac{1}{2} \times 0.1\left(\frac{2 \pi}{2}\right)^2 \times(0.03)^2 \\ & =\frac{1}{2} \times 0.1 \times \pi^2 \times(0.03)^2 \text { Joule } \end{aligned} $
$ \begin{aligned} & =\frac{1}{2} m(2 \pi n)^2 A^2 \\ & =\frac{1}{2} m\left(\frac{2 \pi}{T}\right)^2 A^2 \because n=\frac{1}{T} \\ \text { Keeping value } & =\frac{1}{2} \times 0.1\left(\frac{2 \pi}{2}\right)^2 \times(0.03)^2 \\ & =\frac{1}{2} \times 0.1 \times \pi^2 \times(0.03)^2 \text { Joule } \end{aligned} $
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