Predict by qualitative arguments whether a pendulum oscillating with larger amplitude will have a period longer or shorter than the period for oscillations with small amplitude. (Consider extreme cases.)

The general equation for the time period, when the pendulum oscillating with large amplitude is,

Here θ_m is the maximum angular displacement and T increases with increasing amplitude. Succeeding terms in the finite series becomes smaller and smaller. The value of time period is greater than that of the period when the amplitude is small. Thus, due to non-linearity of displacement, the time period is greater than the time period when amplitude is linear to restoring force.