- #1
barneygumble742
- 28
- 0
Homework Statement
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).
Homework Equations
I'm a little lost on how to get started with this problem. Could anyone please help?
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