A body of mass 20 g in simple harmonic motion has a dimension of … - Vidyadip

Question

A body of mass 20 g in simple harmonic motion has a dimension of 5 cm and the period is 2 sec. Find the total energy of the particle.

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Answer

Time period $( T )=2 \pi$ second
$\therefore$ Harmonic motion $\omega=\frac{2 \pi}{T}$
$\omega=\frac{2 \pi}{2 \pi}=1 ~\text {radian / sec}$
Maximum velocity $\left(v_{\max }\right)= A \omega$
Here, $a$ is the amplitude of simple harmonic motion.
$v_{\max }=5 \times 1=5 cm / sec$
Total energy of simple harmonic motion $=$ Maximum kinetic energy of simple harmonic motion.
$\begin{aligned}\text { Total energy }= & \frac{1}{2} mv_{\max }^2 \\= & \frac{1}{2} \times 20 \times(5)^2 \\= & 10 \times 25=250 \text { ergs } \\= & 250 \times 10^{-7} \text { joules } \\& \because 1 erg=10^{-7} \text { joule } \\= & 2.50 \times 10^{-5} \text { joules}\end{aligned}$

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