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?

THIS IS PROBLEM 1 and my answer:

For a series 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, and what are the natural and the free oscillation mode frequencies? Provide the results within 1 Hz accuracy.

WORK:

inductive reactance(XL) = (WL) = *2*pi* 80KHz*0.025 H = 1.256*10^5

capacitive reactance (Xc) = 1/(WC) = 1/(2*pi * 80 KHz * 10^-10 F = 1.98 *10^4

Impedence = sqrt ( R^2 + (XL - XC)^ )

= sqrt( ( 5*10^3)^2 + ( 1.256*10^5 - 1.98*10^4)^2)

=1.05*10^5

Explanation / Answer

Frequency of resonance, f = 1/(2*pi*sqrt(L*C))

L = 0.025 H

C = 100*10^-12 F

=> f = 1.00658*10^5 = 100658 Hz

Time period from experimental reading, T = 10*10^-6*5/5

since frequency = 1/T = 100000 Hz

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