A series circuit contains an inductor, a resistor, and a capacitor for which L=H₁ R-1002, and C -0.01F. The voltage E(t)= 10, 10, 0≤t≤5 t20 is applied to the circuit. Determine the instantaneous charge q(t) on the capacitor for t> 0 if g(0) = 0 and q'(0) - 0. Problem 2 Find the bilateral Laplace transfrom of the following signal: f(t)-, otherwise Problem 3 Consider the following discrete time system: az ¹ x(z) Y(z) a. Show that the difference equation model is Y[n]– ay[n – 1] = ax[n-1] b. Find the transfer function of the system. c. Find the inpulse response of the system. Problem 4 a. Find the Fourier transform of the following signal: x(t) = u(t) et sin 2.st b. Consider the following ode: dy(t) + 2y(t) = x(t), y(0) - 0 dt Using Fourier transform, find the transfer function of the system and compute the response to the input x(t) = e¹u(t).