Question

Use Runge-Kutta(4th order) method to solve the differential equation for a forced, damped SHO given by

dx²/dt² + $\gamma$dx/dt + $\omega$₀²x = Acos$\omega$t

Choose appropriate values for the constants. By changing the value of $\omega$ in comparison with $\omega$₀ , demonstrate resonance. The initial conditions could be x(0)=0, $\dot{x}$(0)=0. Plot the displacement as a function of time.