A network consisting of a finite number of linear resistor (R), inductor (L), and capacitor (C) elements, connected all in series or all in parallel, is excited with a source of the form
$$\sum_{k=1}^{3} a_k\cos(k\omega_0t) ,\text{where } \thinspace a_k\neq 0, \omega_0\neq0$$
The source has nonzero impedance. Which one of the following is a possible form of the output measured across a resistor in the network?
- $\sum_{k=1}^{3} b_k\cos(k\omega_0t+\phi_k) , \text{where } \thinspace b_k\neq a_k, \forall k \\$
- $\sum_{k=1}^{4} b_k\cos(k\omega_0t+\phi_k) , \text{where } \thinspace b_k\neq 0, \forall k \\$
- $\sum_{k=1}^{3} a_k\cos(k\omega_0t+\phi_k) \\$
- $\sum_{k=1}^{2} a_k\cos(k\omega_0t+\phi_k)$