A simple harmonic oscillator, of mass m and natural frequency ωo, experiences an oscillating driving force f(t)=m a cos(ωt). Therefore, its equation of motion is
d2x/dt2 + ωo2x =αcos(ωt)
where x is the position. Given that at t=0 we have x=dx/dt=0, find the function x(t). Use BOTH with variation of the parameters and guessing methods. Describe the solution if ω is approximately, but not exactly, equal to ωo. Give an example of a physical system where this happens.