(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Write the differential equation that is equivalent to the transfer function given below. Plot y(t). Assume that r(t) = 4t[tex]^{2}[/tex]

Y(s) = 2s[tex]^{4}[/tex]+3s[tex]^{3}[/tex]+2s[tex]^{2}[/tex]+s+1

R(s) = 2s[tex]^{5}[/tex]+3s[tex]^{4}[/tex]+2s[tex]^{3}[/tex]+2s[tex]^{2}[/tex]+4s+2

The transfer function is Y(s)/R(s).

2. Relevant equations

I'm a little lost on how to get started with this problem. Could anyone please help?

3. The attempt at a solution

Given r(t), I thought of converting it to LaPlace and then multiplying it with the numberator so I would be left with Y(s) = numerator / denominator. After that I'll have a mess that I don't think will factor without imaginary numbers. I'm thinking of using partial fraction expansion.

OR

I could have it in this form:

Y(s) [2s[tex]^{5}[/tex]+3s[tex]^{4}[/tex]+2s[tex]^{3}[/tex]+2s[tex]^{2}[/tex]+4s+2] = R(s) [2s[tex]^{4}[/tex]+3s[tex]^{3}[/tex]+2s[tex]^{2}[/tex]+s+1]

and then convert each item to the time domain and then put it back in the transfer function form. However if I did this, then what about the final r(t) = 4t[tex]^{2}[/tex] that's left over?

Thanks,

BG742

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# Homework Help: Transfer function to differential equation

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