part d and e only please

Question 3 Consider an RLC circuit which consists of a resistor, an inductor, and capacitor in series with a voltage source. The response of the RLC circuit is given by the following 2nd order ODE: 9j + 6y + y = f y(0) = A, y(0) = B, where y(t) denotes the charge in the circuit and f(t) is the voltage source for t > 0. a) Express Y(s) in terms of F(s). Y(s) is the Laplace Transform of y(t) and F(s) is the Laplace Transform of f(t). terms, where one of b) Find the values of A and B such that Y(s) can be expressed as a sum of the terms is 1/9 s+1/3 c) Find y(t) for the case in part b). d) Let the voltage source f(t) comprise the following functions: an impulse Dirac delta function applied first at t = 5, then followed by sint applied over 7 st S 10. (Hint: Use the relevant identity in Formulae 27 of the Formula Sheet). i. ii. Sketch f(t) using MATLAB over 0 st 5 15. Find F(s). e) Use your result from part c) to determine y(t) for the case when the voltage source is simply a constant: f(t) = 1/9. Use MATLAB to sketch y(t) over 0 st 5 15. Question 3 Consider an RLC circuit which consists of a resistor, an inductor, and capacitor in series with a voltage source. The response of the RLC circuit is given by the following 2nd order ODE: 9j + 6y + y = f y(0) = A, y(0) = B, where y(t) denotes the charge in the circuit and f(t) is the voltage source for t > 0. a) Express Y(s) in terms of F(s). Y(s) is the Laplace Transform of y(t) and F(s) is the Laplace Transform of f(t). terms, where one of b) Find the values of A and B such that Y(s) can be expressed as a sum of the terms is 1/9 s+1/3 c) Find y(t) for the case in part b). d) Let the voltage source f(t) comprise the following functions: an impulse Dirac delta function applied first at t = 5, then followed by sint applied over 7 st S 10. (Hint: Use the relevant identity in Formulae 27 of the Formula Sheet). i. ii. Sketch f(t) using MATLAB over 0 st 5 15. Find F(s). e) Use your result from part c) to determine y(t) for the case when the voltage source is simply a constant: f(t) = 1/9. Use MATLAB to sketch y(t) over 0 st 5 15