A forced damped spring-mass system (Figure) has the following ordinary differential equation of motion:

Where x = displacement from the equilibrium position, t = time, m = 2 kg mass, α = 5 N/(m/s)², and k 6 N/(m/s)². The damping term is nonlinear and represents air damping. The forcing function F_α sin (ωt)has values of F_α = 2.5 N and ω = 0.5 rad/sec. The initial conditions are

Initial velocity             dx/dt = 0 m/s

Initial displacement     x = I m

Solve this equation using a numerical method over the time period 0 ≤ t ≤ 15 s. Plot the displacement and velocity versus time, and plot the forcing function on the same curve. Also, develop a separate plot of velocity versus displacement.

dx dx +a dt di dr? + kx = F, sin(wr)