A mass-spring system with damping consists of a 9-kg mass, a spring with spring constant3 N/m, a frictional component with damping constant 5 N-sec/m, and an external forcegiven by f(t) = 15 cos (11t) N. Using a 20- resistor, construct an RLC series circuit that isthe analog of this mechanical system in the sense that the two systems are governed bythe same differential equation.Identify the inductance, capacitance, and voltage source required for the RLC circuit.L= henry, C =farad, and E(t) =volt

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Answered: A mass-spring system with damping…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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In practical terms, a damper does not actually behave linearly therefore linearization process is expected. Explain the linearization process of nonlinear damper and how it is done.
The characteristics equation of a closed loop system is s2+4s+16 = 0. The natural frequency of oscillation and damping constant respectively ?
A charging RC circuit has a switched-control DC voltage source of 6V and has a series RC of 20 ohms and 10 microfarads. Determine the following: a. T: Time Constant b. vR at t c. VC at t d. iC at t
4) For the circuit in figure a) What is the relation between Icharging and q? b) Write down Kirchoff's potential law clockwise around the circuit in terms of the variables q and dq/dt. c) Seperate the differential equation so that it is ready to integrate. Do not integrate. Switch S. Vs 5) For the circuit in figure a) Write down Kirchoff's current law at the point e. b) Write down Kirchoff's potential law around the loop abcdea. c) Write down Kirchoff's potential law around the loop abcdefgha. Do not solve the equations 4=18 V 0.50 250 S. S150 050
Learning Goal: To understand the dynamics of a series R-C circuit. Consider a series circuit containing a resistor of resistance R and a capacitor of capacitance C connected to a source of EMF & with negligible internal resistance. The wires are also assumed to have zero resistance. Initially, the switch is open and the capacitor discharged. (Figure 1) Let us try to understand the processes that take place after the switch is closed. The charge of the capacitor, the current in the circuit, and, correspondingly, the voltages across the resistor and Figure R ww io=0 90=0 1 of 1 In the steady state, what is the charge q of the capacitor? Express your answer in terms of any or all of E, R, and C. ▸ View Available Hint(s) [Π| ΑΣΦ q= Submit Part G How much work W is done by the voltage source by the time the steady s- Express your answer in terms of any or all of E, R, and C. ▸ View Available Hint(s) W = ? [VD ΑΣΦ ?
Propose set of differential equations that fully describe the behavior of the system shown in Figure a) Use the force-current analogy to describe the problem and obtain the equivalent circuit. B. m B, Gm J. Tm, Wm,Om Te ,We ,0. J. Bg Be N2 Note: I am giving to the initial circuit, you should explain in detail how to get it. b) Obtain the reduced circuit. c) Using Kirchhoff laws for circuits find the electric circuit's dynamics. d) Replace the analogy equivalents and obtain the electromechanical system's dynamics.
If /1 goes to the right through R1, 12 goes to the right through R2, and /3 goes to the right through R3, what is the resulting equation resulting from applying Kirchhoff's junction rule at point b? Please show solution not only ansSwer. 8.0V R 9.0 V a
2. Find the differential equation to be solved by the following analog computer circuit. Resistors are in the order of MQ, capacitors are in the order of uf. So, start the solution with RC-1 acceptance. is the voltage at point C. (Make the solution in detail. Explain how the stress values at points A, B, D, E and F are found.) 0,5 ww 0,5 ww 12V Hit www me D
Draw the indicated circuit under steady state conditions d/dt = 0 and determine the stored energies. Given: L1= 1 h R1=R2=R3= 1ohm V1= 5v C1=C2= 1F
A 10-ohm resistor and 10 H inductor are connected in series across a source of 12 V. If the current is initially zero, find the current at the end of 5 ms. (Solve using differential equations)
nt d at in figure 2. R, L, V.,, The external source is an AC source with VAC(t) are arbitrary positive constants. 3. R 0000 = Vo cos(nt + p). Figure 2: 'R+LC' circuit with an external source. (a) Find the differential equation that describes the current in the inductor. You can use all what you learned about this circuit in PS2 but show again your work, including Kirchhoff equations. Remember to have sum of potentials to set the differential equation equal to V(t). Hint: just the differential equation. Do not solve it yet. (b) Find IL(t) ignoring the transient behavior. That is, get the steady response to the external source 4. Hint: one way is to set IL(t) = A cos nt + B sin nt, with A, B some constants. Then, find A, B by solving the differential equation of Ir(t). Some suggestions from class: i/ do not use a coefficient of 1 in the Ï term. Use instead (RLC)Ï. The algebra will have less fractions. ii/ Beware that V(t) has an arbitrary phase: . Use cos(nt + p) = cos Nt coso - sin Nt…

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