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**[SOLVED] Graphing a Heaviside unit function**

**1. Homework Statement**

find solution of the following differential eq and graph it:

[tex] y'' + 4y = \delta(t-2\pi)[/tex]

[tex]y(0)=0[/tex]

[tex]y'(0)=0[/tex]

**2. Homework Equations**

[tex] \delta[/tex]

is the Dirac delta function

[tex] u_{c} [/tex]

is the Heaviside unit step function

**3. The Attempt at a Solution**

I used the laplace transform and found the solution to be:

[tex]\frac{1}{2}u_{\pi}(sin(2(t-\pi)))-\frac{1}{2}u_{2\pi}(sin(2(t-2\pi)))[/tex]

which i checked and it is right. However, I'm not sure how to graph this. The following is what I have:

before t = pi and after t = 2pi, y = 0.

But, in between what will it be? If anyone could please help me out I would greatly appreciate it.