Question 226: Oscillations

Question

At a place, the length of the oscillating simple pendulum is made $\frac{1}{4}$ times keeping amplitude same then the total energy will be

Accepted Answer

Total energy of simple pendulum
$$ E=\frac{1}{2} m \omega^2 A^2 $$
Where, angular frequency $\omega=\sqrt{\frac{\mathrm{g}}{l}}$
$$ \begin{aligned} & 	ext { new length }=1 / 4 \ & \begin{aligned} 	herefore \omega_{	ext {new }} & =\sqrt{\frac{g}{l} / 4}=\sqrt{\frac{4 g}{l}}=2 \omega \ 	herefore  E_{	ext {new }} & =\frac{1}{2} m(2 \omega)^2 A^2 \,\,\,\,\,
	ext { ( } \because \mathrm{A} 	ext { is same) }
\ & =4\left(\frac{1}{2} m \omega^2 A^2ight) \ & =4 	imes E \end{aligned} \end{aligned} $$
$$ 	herefore $$ Total energy becomes 4 times

Answer

2 times

Answer

4 times

Answer

8 times

Answer

16 times

Oscillations

At a place, the length of the oscillating simple pendulum is made \frac{1}{4} times keeping amplitude same then the total energy will be

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