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
[tex]A=A_{0}e^{\dfrac{-t}{2\tau}}[/tex]
Put the value into the formula
[tex]5.10=6.00e^{\dfrac{-25.0}{2\times\tau}}[/tex]
[tex]e^{\dfrac{-25}{2\times\tau}}=\dfrac{5.10}{6.00}[/tex]
[tex]e^{\dfrac{-25}{2\times\tau}}=0.85[/tex]
[tex]\dfrac{25}{2\tau}=0.1625[/tex]
[tex]\dfrac{1}{\tau}=\dfrac{0.1625\times2}{25}[/tex]
[tex]\dfrac{1}{\tau}=0.013[/tex]
[tex]\tau=\dfrac{1}{0.013}[/tex]
[tex]\tau=76.92\ sec[/tex]
Hence, The time constant is 76.92 sec.
