# electric engineering question

Anonymous

### Question Description

i need you to write a lab report not that formal it should be basic and solve the circuit by 2nd order of differential equation everything you need u will find it down below , such as the equation and everything else

please reed it carefully before u bit

it should not be that long 3 pages it is good

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StraightTutor
School: University of Maryland

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Lab report

1

Lab Report
Studentβs Name
Institution

Lab report

2

Introduction
To solve the circuit by second order differential equation, then second order circuit is required.
This cuicuits often include the capacitor, inductor, and the resistor all connected in parallel or in
series to be in second order circuits. The figure below show the second-order circuits which are
driven by the forcing function or input source.

By measuring the voltage of the capacitor (Vo), the values obtained are for the frequency of
oscillation, the damping ratio, the time constant of the decay envelope, and the resonant
frequency for different resistances. An op amp circuit will is developed in order to obtain an
output equal to 1000β¦ RLC circuit, without utilizing inductors representing the least essential
elements within the RCL circuit. Without using Ξ± and Ο for the 100 β¦ RLC circuit, the expected
results from the experiments should closely follow the theory, with the op amp circuit having
minimal errors than those of 1000 β¦ RLC circuit.
Theory
In the circuit show below, to solve output voltage loop is used to get the formula 1.
Vo(t) = Vi(t) βRI(t) L(di(t)/dt) [formula 1]
The current can also be solved using formula 2 as shown below.
I(t) = C (dVo(t)/dt) [formula 2]

Lab report

3

Combining formula 2 into formula 1, the following equation is obtained.
LC (d2tVo(t)/dt2) + RC (dtVo(t)/dt) + Vo(t) = Vi(t) [formula 3]
This third formula can be used for homogenious and particular solutions. To use this equation,
we first set Vi(t) equated to zero and Vo equated to Voh, to get formula 4. Formula 5 is then
substituted into formula 4 to arrive at formula 6, which can be simplified to formula 7 shown
below.
LC (d2tVoh(t)/dt2) + RC (dtVoh(t)/dt) + Voh(t) = 0 [formula 4]
Voh(t) = Aest[formula 5]
LCS2Aest+ RCSAest+ Aest= 0 [formula 6]
S2+ (R/L)S + (1/LC) = 0 [formula 7
Formula 7 is then rewritten in the damping ratio, ΞΆ,equal to (R/2L) * (LC)(1/2) and resonant
frequency, with is equal (1/LC)(1/2) to arrive at formula 8 below
S^2 + 2ΞΆ,Οo s + Οo2= 0 [formula 8]

The same equation c...

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