Question

14. A simple pendulum oscillates, the amplitude of
oscillation is reduced to one third of its initial
amplitude A, at the ends of 10 oscillations. After
complete 20 oscillations, its amplitude must be​

Answer 1

Answer:

Amplitude will be 1/9 of its initial amplitude.

Explanation:

For damped oscillations, the amplitude is given by

$\boxed{A=A_0e^{-\alpha t}}$

Where $A_0$ is the initial amplitude and $\alpha$ is the damping factor

For 10 oscillations

$A_1=A_0e^{-\alpha t}$

$\implies \frac{A_0}{3}=A_0e^{-\alpha t}$

$\implies e^{-\alpha t} =\frac{1}{3}$

for 20 oscillations the time will be 2t

Thus

$A_2=A_0e^{-\alpha 2t}$

$\implies A_2=A_0(e^{-\alpha t})^2$

$\implies A_2=A_0(\frac{1}{3})^2$

$\implies A_2=\frac{A_0}{9}$

Thus its amplitude will be 1/9 of its initial amplitude.

Hope this helps.

Answer 2

Explanation:

I thinku will get it

thank u