The switch has been in position 1for a long time and abruptly changes to position 2 at t = 0. If time t is in seconds, the capacitor voltage V_C (in volts) for t>0 is given by

In the given circuit, each resistor has a value equal to 1 Ω.

What is the equivalent resistance across the terminals a and b?

The energy of the signal x(t) =$${{\sin (4\pi t)} \over {4\pi t}}$$ is ___________.

The Discrete Fourier Transform (DFT) of the 4-point sequence
$$x\left[ n \right]$$= {x[0], x[1], x[2], x[3]}
= {3, 2, 3, 4 } is
x[k] = {X[0], X[1], X[2], X[3]}
= {12, 2j, 0, -2j }
If $${X_1}$$ [k] is the DFT of the 12- point sequence$${X_1}$$[n] = {3, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0 },
The value of $$\left| {{{{X_1}[8]} \over {{X_1}[11]}}} \right|$$ is-----------------------.