A simple pendulum of length swings with small angular amplitude

PHYSICS · Multi-part · Fermi University Physics · Mechanics & Dynamical Systems · Plasma Physics · The plasma state and single-particle motion

Plasma Physics, Ch Slow changes and what survives them: adiabatic invariants, mirrors and trapped orbits

Problem

A simple pendulum of length L1=0.40 mL_1 = 0.40\,\mathrm{m} swings with small angular amplitude θ1=8.0∘\theta_1 = 8.0^\circ. Its length is slowly increased (over many periods) to L2=1.60 mL_2 = 1.60\,\mathrm{m}, four times the original length, with g=9.8 m s−2g = 9.8\,\mathrm{m\,s^{-2}}. ((a)) Find the new angular frequency ω2\omega_2. ((b)) Find the ratio E2/E1E_2/E_1 of the new small-oscillation energy to the old. ((c)) Find the new angular amplitude θ2\theta_2.

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