Question

A simple pendulum is swinging with an amplitude of 30cm and a period of 3.50s. what will be the pendulum's period if it's length is extended by 20% the mass is doubled, and the swing has an amplitude of 20cm.

Answer 1

$T=2\pi\sqrt{\frac{l}{g}}\to l=\frac{T^2\cdot g}{4\pi^2}=\frac{3.5^2\cdot 9.81}{4\cdot3.14^2}=3m$

So,

$\sin\alpha=0.3/3=0.1\to \alpha\approx5.7°$

The period of oscillation of a simple pendulum does not depend on the mass of the pendulum and the amplitude (if the angle of deviation of the pendulum does not exceed 6 °)

if the length is extended by 20% then $l_1=l+0.2l=1.2l$

We get that

$\frac{T}{T_1}=\frac{1}{\sqrt{1.2}}\to T_1=\sqrt{1.2}T=\sqrt{1.2}\cdot3.50=3.8s$