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[SOLVED] Graphing a Heaviside unit function
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]
[tex] \delta[/tex]
is the Dirac delta function
[tex] u_{c} [/tex]
is the Heaviside unit step function
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.
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]
Homework Equations
[tex] \delta[/tex]
is the Dirac delta function
[tex] u_{c} [/tex]
is the Heaviside unit step function
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.