Question

A simple pendulum consists of a 1.00-kg bob on a string 1.00 m long. During a time interval of 25.0 s , the maximum angle this pendulum makes with the vertical is found to decrease from 6.00 ∘ to 5.10 ∘.

Answer 1

The time constant is 76.92 sec.

Step-by-step explanation:

Given that,

Mass of bob = 1.00 kg

String length=1.00 m

Time = 25.0 s

Suppose we need to calculate the numerical value of the time constant τ.

We need to calculate the numerical value of the time constant τ

Using formula of time constant

`A=A_(0)e^{(-t)/(2\tau)}`

Put the value into the formula

`5.10=6.00e^{(-25.0)/(2*\tau)}`

`e^{(-25)/(2*\tau)}=(5.10)/(6.00)`

`e^{(-25)/(2*\tau)}=0.85`

`(25)/(2\tau)=0.1625`

`(1)/(\tau)=(0.1625*2)/(25)`

`(1)/(\tau)=0.013`

`\tau=(1)/(0.013)`

`\tau=76.92\ sec`

Hence, The time constant is 76.92 sec.