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(Solved): Problem 2) (20 points) Determine the output \( y(t) \) of the continuous-time ...
Problem 2) (20 points) Determine the output \( y(t) \) of the continuous-time (CT) linear time-invariant (LTI) system described by the following differential equation \[ \frac{d^{2} y(t)}{d t^{2}}+7 \frac{d y(t)}{d t}+10 y(t)=x(t) \] for the input \( x(t)=e^{-4 t} u(t) \). The initial conditions are \( y(0)=3 \) and \( \frac{d y(0)}{d t}=1 \).
Expert Answer
Given that-> d2y(t)dt2+7dy(t)dt+10y(t)=x(t)x(t)=e?4tu(t)So, d2y(t)dt2+7dy(t)dt+10y(t)=e?4tu(t)y(0)=3anddy(0)dt=1 Now apply laplace transform we get->