(Solved): Generate a Pythhon code to solve the following second-orde differential equation with RK4 method. An ...

25.16 The motion of a damped spring-mass system (Fig. P25.16) is described by the following ordinary differential equation: $m\frac{d^{2}x}{d{t}^2}+c\frac{dx}{dt}+kx=0$ where $x=$ displacement from equilibrium position $(\mathrm{m}),t=$ time (s), $m=20?\mathrm{kg}$ mass, and $c=$ the damping coefficient $(\mathrm{N}?\mathrm{s}/\mathrm{m})$. The damping coefficient $c$ takes on three values of 5 (underdamped), 40 (critically damped), and 200 (overdamped). The spring constant $k=20\mathrm{N}/\mathrm{m}$. The initial velocity is zero, and the initial displacement $x=1\mathrm{m}$. Solve this equation using a numerical method over the time period $0?t?15\mathrm{s}$. Plot the displacement versus time for each of the three values of the damping coefficient on the same curve.