Forced vibrations with damping

Consider the motion of an object in a spring-mass system with damping, under the influence of a periodic forcing function $F(t)=F_0\cos(\omega t)$, so that the equation of motion is $$my''+cy'+ky = F_0\cos(\omega t).$$

Simulation

With the following simulation you can analyse the motion of an object in a spring–mass system with damping, subject to an external force $F(t)=F_0\cos(\omega t)$. The simulation also displays the solution of the initial value problem $$m y''+cy'+ky=F_0\cos(\omega t),\quad y(0)=y_0,\quad y'(0)=v_0.$$

Things to try:

• Use controls to start simulation.
• Change the variables:
  • m=mass
  • k=spring constant
  • c=damping
  • F_0=force
  • $\omega$= frequency
• Change the initial conditions $y(0)$ and $y'(0)$.

Note: $\omega_0=\sqrt{k/m}$.