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The expected resonant frequency the system can calculated frac

OBJECTIVE

THEORY

$$K = \frac{1}{2}LI^{2}$$

This energy cycles back and forth between forms, creating an oscillatory pattern, given that the system is isolated and does not lose any energy.

The solution being: I(t) = Imaxsin (ωt+φ)

In addition, the expected resonant frequency of the system can be calculated as:

RESULTS

Inductors L / mH R / Ω
Coil 22.5 7.5
Solenoid 7.62 1.7
Cgreen, Lcoil ω / radians/s ω’ / radians/s f / 1/s f’ / 1/s
Experimental 685 664.415 109.021 105.745
Theoretical 689.819 669.382 109.788 106.536
% Difference 0.7 % 0.7 % 0.7 % 0.7%
Cblue, Lcoil ω / radians/s ω’ / radians/s f / 1/s f’ / 1/s
Experimental 997 982.971 158.677 156.445
Theoretical 971.400 956.996 154.603 152.311
% Difference 2.6 % 2.7 % 2.6 % 2.7 %

image1.png

Figure 1 - Green Capacitor and Coil

image4.png

Figure 4 - Blue Capacitor and Solenoid

DISCUSSION QUESTIONS

  1. What makes the sine wave amplitude decreasing so fast that you have a few oscillations only?

We only obtained a few oscillations due to damping caused by the resistor. The damping constant, B=R/2L, is very large in this experiment, meaning that the amplitude of the wave will decrease very rapidly, as evidenced in the results.

CONCLUSION

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