Question

Can a pendulum with an angular displacement of 20 degrees be considered a simple pendulum?

Answer 1

No. When the angular displacement is 20 deg. then the pendulum cannot be considered as simple pendulum.

This is because we assume uniform motion and ignore the resistance provided by air, called drag. If the angular displacement is increased from 5 deg, then these forces cannot be ignored.

Another reason is trigonometry. To make calculations simple, we make the angle small so that we can use -

sin tan

If the angle is large, the difference in these values will be more and we cannot use. So, in that case the pendulum will not be a simple pendulum.