Period and amplitude dependence for a pendulum?

Question

Does the period of a pendulum depend on amplitude?

a) Yes

b) No

c) It depends, for small amplitudes, no, but for large amplitudes, yes (to within fractions of a second)

d) It depends, for small amplitudes, yes (to within fractions of a second), but for large amplitudes, no

I think it would be c, but I'm not completely sure. An explanation would be very helpful.

Answer 1

For relatively small amplitudes, the period (T) of a pendulum is found by:

So it only depends on the length (L)

HOWEVER, when amplitude gets big, it does depend on the amplitude. So the answer is C

Answer 2

William W is absolutely correct. The equation for the restoring force = mg sin θ. For it to be true SHM the restoring force must be directly proportional to the displacement. If the angle is in radians Sine θ is close to θ if the angle is less than 15 degrees (less than 1% error). If the angle exceeds this, the motion is still periodic but not simple harmonic