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

Answer:

The time constant is 76.92 sec.

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

$A=A_{0}e^{\dfrac{-t}{2\tau}}$

Put the value into the formula

$5.10=6.00e^{\dfrac{-25.0}{2\times\tau}}$

$e^{\dfrac{-25}{2\times\tau}}=\dfrac{5.10}{6.00}$

$e^{\dfrac{-25}{2\times\tau}}=0.85$

$\dfrac{25}{2\tau}=0.1625$

$\dfrac{1}{\tau}=\dfrac{0.1625\times2}{25}$

$\dfrac{1}{\tau}=0.013$

$\tau=\dfrac{1}{0.013}$

$\tau=76.92\ sec$

Hence, The time constant is 76.92 sec.