A simple pendulum of length 1.00m is pulled aside so that the string makes an angle of 20∘ with the vertical and is then released from rest.
(a) Calculate the exact magnitude of the tangential component of the gravitational force acting on the bob at this initial position.
(b) Using the small–angle approximation, find the value you would obtain for the restoring force at the same displacement.
(c) Determine the percentage error introduced by using the small–angle approximation.
(d) Comment on whether the approximation is acceptable for precise timekeeping applications at this amplitude.