Discussion:
Equation of motion, functions
Q: A simple harmonic oscillator, of mass m and natural frequency w_0, experiences an oscillating driving force f(t)=m a cos(wt). Therefore, its equation of motion is
d2x/dt2 + w20x = acos(wt)
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 w is approximately, but not exactly, equal to w_0. Give an example of a physical system where this happen