2.1 The periodic function f(t) has the line spectrum shown in Figure P2.1. Assuming that f(t) is an even function, determine the following:
(a) The trigonometric Fourier series for f(t).
(b) The complex Fourier series for f(t).
2.2. Find v(t) in the circuit of Figure P2.2 using the Laplace transform.
2.3. Find x(t) for t0 for
d2x(t)/dt2 + x(t) = 0
where x(0) = 1 and dx(0)/dt = −1.
2.4. Consider the Laplace transform
Using the final-value theorem, determine f(∞). Check your answer by finding the inverse Laplace transform f(t) and letting t → ∞.
2.5. The initial conditions for the following differential equation
are given by
(a) Write in its simplest form the Laplace transform of the function Y(s), by taking the Laplace transform of this differential equation.
(b) Expand Y(s) by means of the partial fraction expansion method. Determine all unknown constants. ...