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
[tex]\theta=\theta_{0}e^{\dfrac{t}{\tau}}[/tex]
Where, [tex]\theta[/tex] =amplitude
[tex]\theta_{0}[/tex] =amplitude at t = 0
Put the value into the formula
[tex]2.5=15e^{\dfrac{-1000}{\tau}}[/tex]
[tex]\dfrac{1}{6}=e^{\dfrac{-1000}{\tau}}[/tex]
[tex]ln\dfrac{1}{6}=\dfrac{-1000}{\tau}[/tex]
[tex]\tau=\dfrac{1000}{-ln\dfrac{1}{6}}[/tex]
[tex]\tau=558.11\ sec[/tex]
Hence, The value of the time constant is 558.11 sec.
