Higher-order ordinary differential equations
15.1 A simple harmonic oscillator, of mass m and natural frequency ω0, experiences an oscillating driving force f(t) = ma cos ωt. Therefore, its equation of motion is
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 ω is approximately, but not exactly, equal to ω0.
To find the full solution given the initial conditions, we need the ...