When the input x(t) = 5u(t) is applied to a linear second-order circuit the response of the state variable is y(t) = 10e^(-100t)-5e^(-200t) + 5
a) What are the initial conditions y(0) and y'(0)?
b) For the same initial conditions, what is the response when the input is x(t) = 20u(t)?
c) Design a simple RLC circuit that would produce all of these responses.
d) It is claimed that the zero-state response of the circuit for an x(t) = 10e^(-50t)u(t) is y(t) = 10e^(-50t) - 15e^(-100t) + 5e^(-200t)