(Solved): 2. (+10 points) Consider the linear op-amp circuit shown below. (a) Assuming all initial condition ...

2. (+10 points) Consider the linear op-amp circuit shown below. (a) Assuming all initial conditions are zero, find the transfer function \( G(s)=V_{0}(s) / V_{\text {in }}(s) \). For full credit, write the transfer function in standard polynomial form (i.e., no fractions in \( s \) in the numerator or denominator). Now assume that \( C=1, R_{1}=1, R_{2}=2, R_{3}=1 \) (unitless quantities). (b) What is the system response \( v_{0}(t) \) to a step input? Hint: Partial fraction expansion may make use of known Laplace transform pairs easier.