A pendulum with a rod of length

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Oscillations and normal modes · Oscillations and normal modes

Modes, Packets and Media, Ch The anharmonic oscillator: frequency, harmonics and drift

Problem

A pendulum with a rod of length L=0.75 mL=0.75\,\mathrm{m}, treated as an ideal pendulum, is released from rest at θ0=75∘\theta_0=75^\circ. Take g=9.8 m s−2g=9.8\,\mathrm{m\,s^{-2}} and the tabulated value K(sin⁡37.5∘)=K(0.6088)=1.7577K(\sin37.5^\circ)=K(0.6088)=1.7577. ((a)) Find the small-amplitude period T0T_0 and the exact period T=(4/ω0)K(k)T=(4/\omega_0)K(k). ((b)) Find the period from the two-term series T/T0=1+θ02/16+11θ04/3072T/T_0=1+\theta_0^2/16+11\theta_0^4/3072, and its relative error against the exact value.

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