Show that x(t) = x 0 sin(ωt) is a solution of the undamped harmonic oscillator differential equation at small angles d2x(t)/dt2 = −ω2x(t). Also, show that x(t) = x0e−γ t/2 cos(ωt) is a solution of the damped harmonic oscillator equation d2x(t)/dt2 = −ω2x(t) − γ [dx(t)/dt]. You may assume γ2 ≪1.
Show that x(t) = x
0 sin(ωt) is a solution of the undamped harmonic oscillator differential equation at small angles d2x(t)/dt2 = −ω2x(t).
Also, show that x(t) = x0e−γ t/2 cos(ωt) is a solution of the damped harmonic oscillator equation d2x(t)/dt2 = −ω2x(t) − γ [dx(t)/dt]. You may assume γ2 ≪1.
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