For the electrical circuit shown below when the switch K is closed the charge and current are observed to oscillate (Fig. 14.2). Show that the differential equation governing the charge of the system can be written as d2Q/dt2+2ydQ/dt+w0^2Q=0 where y and w0^2 are to be determined in terms of the capacitance, C , inductance, L , and resistance, R. For a resistance R = 100 S, capacitance C = 700 pF and inductance L = 80 mH calculate (a) The natural frequency, f0 , of the oscillation. (b) The time constant, t , for the decay.
Solution:
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