Experimentally, the free oscillation mode frequency is obtained by a read out fr

Question

Experimentally, the free oscillation mode frequency is obtained by a read out from the oscilloscope screen. A student has found that 5 full periods of the damped oscillations cover 5.0 major divisions on the horizontal scale, with time-sweep knob indicating 10 microsecond/division. What is the frequency obtained from the experimental read out? With preserved setting of the oscilloscope (and a time-sweep subdivision being 0.2 of the horizontal division), is it possible to distinguish this read out from the resonance frequency f0 theoretically obtained in Problem 1, and examined experimentally too?

Problem 1 details:

RLC circuit with resistance 5 KOhm, capacitance 100 picoFarad, and inductance 0.025 Henry, what is the inductive and capacitive reactance, and the impedance at frequency 80 kHz

Natural/free oscillation mode frequency= 1/(2pi *sqrt[LC])=1/(2pi* sqrt[0.025H*100*10^-12F])=1.0*10^5 Hz

If I understand correctly, the first question is

T=(10*10-6s)(5 divisions)/5 periods=1*10-5s

f=1/T =1/(1*10-5)= 1*10^5 Hz

but I need help with the second question in bold, please!

Explanation / Answer

T = the time per period and f = 1/T . 10s = 1e-5s so f = 1e5 or 100khz
XL = L = 2f*L = 12,566
XC = 1/C = 19,894
Z = 5000 +j12,566 -j19,894 = 8871 at -55.7 degrees
o = 1/LC = 63,246 Hz Resonance.

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