  The classic simple pendulum is a device which works as a simple harmonic
oscillator (S.H.M.) only approximately. The time period remains fixed as long
as the amplitude is kept sufficiently small. This limitation makes it
unsatisfactory choice for practical time keeping purposes. The question
addressed in this paper is regarding the modifications that can be made to the
pendulum so that its time-period is independent of amplitude. Though the idea
is not new, it is shown using rigorous mathematics that if the length of the
suspension is suitably controlled so as to have a cycloidal path for the bob,
this can be achieved.

Classical Physics