# Laplace Transforms & Transfer Functions

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Compute the transfer function H(s) of the continuous-time system below given by the input/output differential equation.

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By using the Laplace transform, compute the convolution x(t)*v(t) of the two signals where x(t)=e-tu(t) and v(t)=(sin t)u(t):

Using the convolution equation, I had x(t)*v(t) <-> X(s)V(s).

x(t)=e-tu(t) <-> 1/s+1

for v(t)=(sin t)u(t), I had s/s2 with ω = 1, an I came up with X(s)V(s) = s/( s3+s2) The choices are as follows:

1/2e-t+1/2cos(t+45) ½(e-t-cost+sint) (e-t+cost-sint) e-t+1/2cost-1/2sint

Please assist in this calculation.

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Determine the final value of: X(s) = (3s2+4s+1)/(s4+3s3+3s2+2s)

0 1/2 infinity 8/9

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Solution shows how to find the laplace tranform for a differential equation in a Word attachment.

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Compute the transfer function H(s) of the continuous-time system below given by the input/output differential equation.

Solution

Laplace transform's property

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