Chapter 3, Problem 3.42P

An undamped driven harmonic oscillator satisfies the equation of motion m(d²x/dt²+ ω₀²x) = F(t). The driving force F(t) = F₀ sin(ωt) is switched on at t= 0. (a) Find x(t) for t > 0 for the initial conditions x = 0 and v = 0 at t = 0. (b) Find x(t) for ω = ω₀ by taking the limit ω → ω₀ in your result for part (a). Sketch your result for x(t). Hint: In part (a) look for a particular solution of the differential equation of the form x = A sin(ωt) and determine A. Add the solution of the homogeneous equation to this to obtain the general solution of the inhomogeneous equation.