Problem: What are the maximum speed, acceleration, and restoring force for a 1.2 kg bob at the end of a 150 cm cord if the bob is displaced 18o and released?
Solution: This angular displacement is greater than the 5o that forms the boundary between SHM and pendulum motion (for 3-digit accuracy). But it doesn't matter; we won't be using the conclusions based on that assumption. In fact, the solutions don't depend on this chapter's topics at all!
The maximum speed occurs at the bottom of the swing. Using conservation of energy, the potential energy at maximum displacement equals the kinetic energy at the bottom of the swing:
Students often have trouble understanding how to get h:
The maximum force and acceleration occur at the maximum displacement:
So the maximum restoring force is
And the maximum acceleration (tangential acceleration is implied) is this force divided by 1.2 kg = 3.03 m/s2.