Question 2 Not yet answered Marked out of 8.00 Determine the output $C_R(s)$ due to the input $R(s)$, when $R(s)$ is a unit ramp function. $R(s)$ \(\boxed{\times}\) $2s+1$ \(\boxed{\times}\) $\frac{4}{s+1}$ $C(s)$ Select one: Oa. $C_R(s) = \frac{4(2s+1)}{s^2(9s+5)}$ Ob. $C_R(s) = \frac{8(2s+1)}{s^2(5s+9)}$ Oc. $C_R(s) = \frac{4(2s+1)}{s^2(s+5)(s+1)}$ Od. $C_R(s) = \frac{-4(2s+1)}{s^2(3s+5)}$ Oe. $C_R(s) = \frac{4(s+2)}{s^2(7s+5)}$
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The unit ramp function is defined as R(t) = t for t >= 0. The Laplace transform of R(t) is given by: R(s) = L{R(t)} = ∫[0,∞] e^(-st) * R(t) dt Since R(t) = t, we can substitute this into the equation: R(s) = ∫[0,∞] e^(-st) * t dt Now, let's solve this integral. Show more…
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