Show that x(t) = x0 sin(ωt) is a solution of the undamped harmonic oscillator differential equation at small angles d^2x(t)/dt^2 = −ω 2x(t). For 7.5 points of extra credit, instead show that x(t) = x0e^−γt/2 cos(ωt) is a solution of the damped harmonic oscillator equation d^2x(t)/dt^2 = −ω 2x(t) − γ dx(t)/dt . You may assume γ^2<< 1.
Show that x(t) = x0 sin(ωt) is a solution of the undamped harmonic
oscillator differential equation at small angles d^2x(t)/dt^2 = −ω 2x(t). For 7.5 points of extra credit, instead show that x(t) = x0e^−γt/2 cos(ωt) is a solution of the damped harmonic oscillator equation d^2x(t)/dt^2 = −ω 2x(t) − γ dx(t)/dt . You may assume γ^2<< 1.
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