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

The value of the time constant is 558.11 sec.

Step-by-step 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^{(t)/(\tau)}`

Where,
`\theta` =amplitude

`\theta_(0)` =amplitude at t = 0

Put the value into the formula

`2.5=15e^{(-1000)/(\tau)}`

`(1)/(6)=e^{(-1000)/(\tau)}`

`ln(1)/(6)=(-1000)/(\tau)`

`\tau=(1000)/(-ln(1)/(6))`

`\tau=558.11\ sec`

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