Question

A pendulum of length L = 1 m is released from an initial angle of 15° . After 1000 s, its amplitude is reduced to 2.5º. What is the value of the time constant, T?

Answer 1

Answer:

The value of the time constant is 558.11 sec.

Explanation:

Given that,

Pendulum length = 1 m

Initial angle = 15°

Time = 1000 s

Reduced amplitude = 2.5°

We need to calculate the value of the time constant

Using formula of damping oscillation

$\theta=\theta_{0}e^{\dfrac{t}{\tau}}$

Where, $\theta$ =amplitude

$\theta_{0}$ =amplitude at t = 0

Put the value into the formula

$2.5=15e^{\dfrac{-1000}{\tau}}$

$\dfrac{1}{6}=e^{\dfrac{-1000}{\tau}}$

$ln\dfrac{1}{6}=\dfrac{-1000}{\tau}$

$\tau=\dfrac{1000}{-ln\dfrac{1}{6}}$

$\tau=558.11\ sec$

Hence, The value of the time constant is 558.11 sec.