Two ways of solving this problem are shown here. You can choose whichever one makes more sense to you, or seems easiest.

Solution: Alternative 1

We will solve this in the same way as the previous section, 2nd Order Linear DEs.

A.E., Solution is:

The response is critically damped, since the roots are equal.

So we can now write:

Therefore

Solution: Alternative 2

Using the variables given in the damping theory above:

, , , so

So and therefore we have critical damping.

Now

The general solution is given by

So

This is the same solution we have using Alternative 1. The rest of the solution (finding A and B) will be identical.

Solution using SNB:

[Go to Compute menu, Solve ODE..., Exact]

The graph of our solution is: