The following series RLC circuit with zero initial conditions is excited by a unit impulse function $$\delta$$(t). For t > 0, the output voltage V_c(t) is

In the following circuit, the switch S is closed at t=0. The rate of change of current $$\frac{di}{dt}(0^+)$$ is given by

The Thevenin equivalent impedance Z_th between the nodes P and Q in the following circuit is

Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, R3, R4.

Properties

P1 : Linear but NOT time-invariant
P2: Time-invariant but NOT linear
P3: Linear and time-invariant

Relations

R1: y(t) = $${t^2}$$ x(t)
R2: y(t) = t$$\left| {x(t)} \right|$$
R3: y(t) = $$\left| {x(t)} \right|$$
R4: y(t) = x(t-5)