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 31 minutes.

What is the pendulum's time constant?

How much additional time elapses before the amplitude decreases to 25% of its initial value?

Answer 1

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 28 minutes.

What is the pendulums time constant?

How much additional time elapses before the amplitude decreases to 25% of its initial value?

A = A0 * e^-t / k   where k is the time constant
A / A0 = 1/2 = e^-t / k
ln 1/2 = -t / k
k = -28 / ln 1/2 = 40.4 min
1/4 = e^-t/40.4
-t / 40.4 = ln .25
t = 56 min    or an additional 15.6 mim