we calculated the values we need, and measured the capacitor and resistor we used in lab. The experimental value for R is 3 and for C is 414uF.We are not able to measure the inductance. We assume it is correct.
we can see that our circuit is underdamped. We also calculated the value we need to make it critically damped.

This is the circuit we are going to build

true circuit
output function. We can see it is under damped.

From the measurements, time between two peak is 120us, so the wd=2PI/t=5*10^4.which has almost 90% difference from the value we calculated before.
Summary:
Today, we learn how to solve source free RLC circuit. We also learn how to determine whether the circuit is over damped, underdamped, or critically damped. We do a lab of a underdamped circuit, and we get a big percent difference which is almost 100%. Possible causes of error could be the way we measure the circuit, or could from our input value.
The results are significantly different from what we expected, that may due to the difficult of measure time, the resistance of inductor, we observed that the small change of resistor could significantly change the results since the resistance in this set up is so small.

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