Time Period for Pendulum

Question

For an object that is attached to a string and sways back and forth (pendulum), does the time period depend on the angular amplitude of the oscillation?

Answer 1

Short answer is "no". Usually when we mention a pendulum in introductory physics a key point is that the period only depends on the length of the string. The object's mass and the amplitude are irrelevant. It is an interesting and useful feature of a simple pendulum.

Longer answer is "technically, yes". There are a lot of assumptions that go into that "no" answer, such as that air resistance, friction, stretchiness of the string, mass of the string, and other real things are all zero. Even then, the period is approximately independent of the angular amplitude, and even that's only true for small angles (rule of thumb less than 15^o).

Good to consider what level your teacher/professor is aiming at.

Best answer may be that "for small angles the period of an ideal simple pendulum has neglible dependence on the angular amplitude".

Answer 2

Yes it depends on the angular displacement ( theta)

For only small angular displacement it is

T = 2pi sqrt( i/g)

Where l = length and g = acceleration due to gravity