7. A simple harmonic oscillator, of mass m and natural frequency wo, experiences an oscillating driving force f(t) = ma cos wt. Therefore, its equation of motion is d²x + wix = a cos wt, %3D dt² where x is its position. Given that at t 0 we have x = dx/dt = 0, find the function x(t). Describe the solution if w is approximately, but not exactly, equal to wo.

7. A simple harmonic oscillator, of mass m and natural frequency wo, experiences an oscillating driving force f(t) = ma cos wt. Therefore, its equation of motion is d²x + wix = a cos wt, %3D dt² where x is its position. Given that at t 0 we have x = dx/dt = 0, find the function x(t). Describe the solution if w is approximately, but not exactly, equal to wo.