Spring Motion

Part 3: Critical Damping

Now we experiment with the effects of larger values of c.

1. Enter your value of c from Part 2 in place of the default 300 in the description of the differential equation. Plot the solution for your value of c, and then increase c in steps of approximately 500, recording how the solution changes.

2. The value
   
   has a special significance. What is that significance?

3. Calculate this number for your spring system (or ours).

4. What happens to the solution as you approach this value of c?

5. What happens as you pass this value of c?

6. Explain these results in terms of the symbolic form of the solutions.