Forced Spring
Systems
Part 4: Damping (Optional)
In this part we explore the effects of damping on beats and resonance. That is, we study the initial value problem
y'' + c y' + k2
y = F0 cos wt, y(0) =
0, y'(0) = 0,
without assuming that c is 0.
- Explore the implications of damping with c = 1 and the rest of the parameters as before.
- How does damping affect beats?
- How does damping affect near-resonance?
- How does damping affect resonance?
- Find the symbolic solution of the initial value problem
y'' + c y' + k2
y = F0 cos wt, y(0) =
0, y'(0) = 0,
for any c different from 0. Use the symbolic solution to confirm your observations in the three preceding steps.
