INTRODUCTION

It was remarked in the introduction to Exp. 2 that oscillation, or vibration phenomena are among the most common in nature. Nearly as frequent are examples of resonance, where a system of some kind is made to vibrate, not by being "jolted" into vibration, as was our circuit in that Experiment, but rather by coming under the influence of some oscillatory driving force which has just the proper frequency.

In previous experiments and in lectures, you have seen discussion of circuit analysis using the differential circuit equations for time domain solutions and using "phasors" for frequency domain solutions. Experiment 2 measured the time domain response of the LRC circuit to sudden changes in voltage. In this experiment you will measure the frequency domain response of the LRC curcuit to sinusoidal driving currents. The very large response to relatively small applied voltage or current at "resonance" is characteristic of all resonance phenomena. Using an electrical example makes it easy for you to measure and anaylze the response.

Our concern, then, is with an oscillating system consisting of inductance, capacitance, and resistance in series, as we had in the previous experiment. However, we now insert into the circuit a fourth element which is a voltage generator. This component has the property that a sinusoidally oscillating potential exists across its terminals, and its magnitude, frequency, and phase are unaffected by whatever current may flow in the circuit. The circuit may be drawn as shown in Figure 1.

Figure 1

The complete LCR series ciruit is drawn in (a) with all three resistors, including R_S for the Signal Generator, R_L for the Inductor and R_r for the resistor which you put into the circuit. An equivalent circuit is drawn in (b) with the single resistor R (= R_r + R_S + R_L) representing the total of all of the circuit resistance. The internal voltage source, V_S(t), is a sine wave, and the current through all of the components is I.