Chapter 5.7, Problem 23P

The position of a certain lightly damped oscillator satisfies the initial value problem

$y\text{'}\text{'}+0.1y\text{'}+y={\displaystyle \underset{k=1}{\overset{20}{\sum }}{(-1)}^{k+1}\delta (t-k\pi ),}$

$y(0)=0,$ $y\text{'}(0)=0.$

Observe that, except for the damping term, this problem is the same as Problem 18.

a) Try to predict the nature of the solution without solving the problem

b) Test your prediction by finding the solution and drawing its graph.

c) Determine what happens after the sequence of impulse ends