Question

A circuit comprises a 2 henry inductor, a 1/32 farad capacitor, no resistor, and a voltage source of 128 sin 4t volts. NOTE: initial conditions are not needed to do this problem.

(a) Write the governing equation (ODE) for q(t). Do NOT solve the ODE.

(b) Without solving the ODE for q(t), determine the natural frequency of the circuit (with units).

(c) Will the circuit undergo pure resonance? Clearly explain why or why not.

Answer 1

A circuit comprices a and a 2 henry inductor, a 3 farad capacitor, no resistor, voltage source of 128 sinut volts. The differential equation for an electrical circuit is d'alt) + R dq (+) + + 9(+) = E (+) (9) L det? R=0 32 given, L=2 hengy, cata farad. El+): 128 singt volts. putting these values in a d917) +0 091+) + 329(+) = 128 singt dt² at 2 > 2d²q1t) + 2qht) = 128 sinut dtz dividing by 2 '+169(+) = 64 sinut dt² d²qLt). (6) The natural frequency of the circuit is wa - The | 2x Wo wo i 5/16 114 The natural frequency = 4 hertz. (C) Given, The voltage source asinut = 128 sinut .. The frequency w 24 since the circuit will tundergo pure resonance. wo wo