Question

A certain pendulum oscillates back and forth every 3.00s . What would the new period be, in s , if the pendulum were one-half of its original length?

Answer 1

Answer:

2.122 second

Explanation:

T1 = 3 s

L1 = L

L2 = L/2

As we know the time period of a simple pendulum is related by the length of the pendulum as

$T =2\pi \sqrt{\frac{L}{g}}$

Here, only the length of pendulum changes and the value of g is constant so,

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

$\frac{T_{2}}{3} =\sqrt{\frac{L}{2L}}$

T2 = 2.122 second