Modify your numerical integration of the spring–mass system to include the effects of friction. Such a system is called a
“damped oscillator.” Simulate the effect of all three kinds of friction: sliding friction (independent of v), viscous friction
(proportional to v), and air resistance for large blunt objects (proportional to v2). Choose friction to be small enough that you
get at least two full cycles of oscillation, but large enough that you see an effect. If the friction is so large that the graph
never crosses the axis, the system is said to be “over-damped.” For each kind of friction, display the following:
1. Display an animation of the motion of the system.
2. Plot a graph of position vs. time.
3. Plot graphs of K, U, and (K + U) vs. time.
On the energy graphs, when is the energy loss rate large and small, and why?