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.