Physics Pendulum Problem???Please help do not know where to start!?

Question

A physics department has a Foucault pendulum, a long-period pendulum suspended from the ceiling. The pendulum has an electric circuit that keeps it oscillating with a constant amplitude. When the circuit is turned off, the oscillation amplitude decreases by 50% in 25 minutes.

What is the pendulum's time constant?
-I found it to be 53 min. Which Correct

How much additional time elapses before the amplitude decreases to 25% of its initial value?(This is the one I cannot solve)

THANK YOU!

Answer 1

Part B can be solved by using the equation t=(time constant)(ln2)



t=(53)(ln2)

t=(53)(0.693)

t=37 min

Answer 2

Here is how you get the answer for the first part of the problem!



t=37 mins -> 2220sec

We want "T" which is the pendulum time constant



Using this equation

.5A=Ae^(-t/T)



The .5A is half the amplitude



Take ln of both sides to get ride of Ae

=ln(.5)=-2220/T



Now rearrange to = T

T=-2220/ln(.5) = 3202.78sec / 60 secs = 53.38 mins -> first part of the answer.



The second part is really easy. It took 37 mins to decay half way. meaning to decay another half of 50% which equals 25% it will take an additional 37 mins!

Answer 3

How did you get the answer?