Question

Two exactly identical simple pendulums are oscillating with amplitudes 2 cm and 6 cm.Calculate the ratio of their energies

Answer 1

Answer:

1/9

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Answer 2

The ratio of their energies is 1:9.

Explanation:

The motion possessed by the simple pendulum is called simple harmonic motion. the total energy of the pendulum in this case is given by :

$E=\dfrac{1}{2}m\omega^2A^2$

i.e.

The energy is directly proportional to the square of amplitude.

Here, two exactly identical simple pendulums are oscillating with amplitudes 2 cm and 6 cm. So, the ratio of the energies is given by :

$\dfrac{E_1}{E_2}=\dfrac{A_1^2}{A_2^2}$

$\dfrac{E_1}{E_2}=\dfrac{2^2}{6^2}$

$\dfrac{E_1}{E_2}=\dfrac{2^2}{6^2}$

$\dfrac{E_1}{E_2}=\dfrac{1}9}$

So, the ratio of their energies is 1:9. Hence, this is the required solution.

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