A Simple pendulum consists of a small object ( the pendulum bob) suspended from the of a lightweight cord. we assume the cord doesn't stretch and that its mass can be ignored relative to that of the bob. The restoring force is the net force on the bob, equal to the component of the weight, `mg`, tangent to the arc: `F = - mgsinθ` To a very good approximation for small angels, `sinθ≈ x/L` where `x` is the length of arc. `=>` `F ≈ - (mg)/L x` Thus for small displacements , the motion is essentially simple harmonic, since this equations fits Hooke's law, `F = - kx` where `k = (mg)/L` `=>` `T = 2πsqrt(m/k) = 2πsqrt(m/((mg)/L))` Maximum speed `KE + PE =` constant `mgh = 1/2 mv_(max)^2` `=>` `v_(max) = sqrt(2gh)` where `h = L - Lcosθ_0 = L(1-cosθ_0)` `=>`