Question

A simple pendulum is made from an object (called the pendulum bob) of mass m, tied to an ideal string of length L. When the pendulum is set into small angle oscillations, its motion has a period T.

Answer 1

Answer:

(a)The period will increase by 2 times

(b)The period will increase by 2.45 times

Explanation:

(a)$T_{1}=2\pi \sqrt{\frac{m}{k} }$

When the mass increased by a factor of 4 then;

$T_{2}=2\pi \sqrt{\frac{4m}{k} }$

$\frac{T_{2} }{T_{1} }=\frac{2\pi \sqrt{\frac{4m}{k} }}{2\pi \sqrt{\frac{m}{k} }}$

$\frac{T_{2} }{T_{1} }$ =$\sqrt{\frac{4m}{k} }$× $\sqrt{\frac{k}{m}}$

$\frac{T_{2} }{T_{1} }=\sqrt{4}$

$\frac{T_{2} }{T_{1} } =2$

The period is doubled by 2 times

(b) if the pendulum is taken to the moon where the force of gravitation is about g/6 then

$T_{1}=2\pi \sqrt{\frac{l}{g} }$

$T_{2}=2\pi \sqrt{\frac{l}{\frac{g}{6} } }$

$\frac{T_{2} }{T_{1} }=\frac{2\pi \sqrt{\frac{6l}{g} }}{2\pi \sqrt{\frac{g}{l} }}$

$\frac{T_{2} }{T_{1} }=\sqrt{6}$

$\frac{T_{2} }{T_{1} }$=2.45

The period will increase by 2.45 times