$y(t)=Y_m*e,I_d*cos({}_d*t+)$

$(5)$

Where the damping ratio is

$=\frac{*T_d}{2}=\frac{*}{{}_d}$

PROCEDURE

Fig. $1.$ The series RLC circuit. $C=0\mathrm{.}01F,L=10mH$

Construct the series RLC circuit in Figure $1.$

Set the signal generator to the square pulse mode, the amplitude to $100$ V p$.$

Calculate the resonance frequency $f_0$ of the circuit, then adjust the frequency of the signal generator to $10$ times lower than $f_0,$

Set R to $10k$ and connect the oscilloscope to observe the capacitor voltage $($set the time scale to about $5$ to $20s)$ then run the simulation. You may need to run and stop simulation times.

What type of response do we obtain for the voltage?

Save the voltage wave form for your report.

Calculate the value of R for which the response is critically damped.

Set R to the calculated value in step $5$ then run the simulation. Is the waveform corresponds critical damping as expected? Save the waveform.

Adjust R to $500.$ What type of response did you obtain for the voltage? Save your waveform. $10.$ Find $T_d$ the damping period using the cursors and deduce $f_d$ the damping frequency then ${}_d$

From equation $(3)$ calculate ${}_d$ compare this result with ${}_d$

Calculate the error of ${}_d$

Draw your conclusion.