Answer:
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

Where,
=amplitude
=amplitude at t = 0
Put the value into the formula





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