Question

how do you find natural frequency of pendulum? and what kind of assumptions are made?

Answer 1

Assume small amplitude oscillations. Set up Newton's law. You need to work out the tangential component of gravity and show that is a restoring force, proportional to the deflection from the equilibrium position. A linear restoring force is the characteristic of SHM (Simple Harmonic Motion) It means that \(a=-(constant)x\) the constant is \(\omega^2\) where \(\omega=2\pi/T\) is the angular frequency of the oscillations.