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Solve this integral and then plot it?

Posted 8 years ago

Hi, I'm trying to solve this integral but it's been taking time and not giving me the answer. Could you please find me the solution of this integral and help me to plot that. I'll be very thankful to you. Regards

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POSTED BY: Muhammad Afzal
3 Replies
Posted 8 years ago

Please take a look at the attached notebook. The first section of the notebook calculates zero for the value of your integral, which is probably not what you intended. The second section shows an example convolution of two functions.

A trick that I use and that may help you is to start with something similar to what I want, but simple enough that it actually gives an answer. Then I make small changes and re-run the calculation to make sure I am still getting an answer. That way I know exactly where I went wrong, and I can go back and try again. For example, if I want to do a calculation with a damped sine, I might start with a square wave, then change to sine, then put in the damping. If my approach doesn't work with the square wave, I look for places to simplify.

I would not use PiecewiseExpand until I knew the integral was right. Also, I might try integrating just my H[t] to verify it was not the source of the problem. I would take it apart, until I found something so simple that it worked. Then I would build on that.

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POSTED BY: Louis Godwin
Posted 8 years ago

I am looking at H[t] and H[t-tau] in the integral. Since the integral is from 0 to t, I expect t>0 so H[t]=1. Also since the limits of integration give, 0< tau < t , H[t- tau]=1. So the entire integral is zero. You might want to plot your forcing function to make sure it is right.

You might also want to use the built-in HeavisideTheta instead of your H and you should use := in the definition of xd.

I find that adding assumptions to my integrals often helps. Here I would use Assumptions->{t>0, 1>zeta>0, w>0}.

POSTED BY: Louis Godwin
Posted 8 years ago

Hi Louis how you doing? I've tried these assumptions but still getting no answer :(

POSTED BY: Muhammad Afzal
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