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Katen [24]
3 years ago
8

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 pend

ulum is set into small angle oscillations, its motion has a period T.
Physics
1 answer:
vlabodo [156]3 years ago
7 0

Answer:

<em>(a)The period will increase by 2 times</em>

<em>(b)The period will increase by 2.45 times</em>

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

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