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HW 4

The document outlines a homework set for ME3017 at Georgia Institute of Technology, due on February 20, 2025. It includes problems related to circuit analysis, including finding capacitor voltages, deriving differential equations, and using state variable models. Additionally, it involves numerical simulations using Matlab or Simulink for specific circuit responses and calculations related to a robot arm's dynamics.

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5 views1 page

HW 4

The document outlines a homework set for ME3017 at Georgia Institute of Technology, due on February 20, 2025. It includes problems related to circuit analysis, including finding capacitor voltages, deriving differential equations, and using state variable models. Additionally, it involves numerical simulations using Matlab or Simulink for specific circuit responses and calculations related to a robot arm's dynamics.

Uploaded by

lineric477
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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George W.

Woodruff School of Mechanical Engineering


Georgia Institute of Technology

ME3017 HW SET #4 Due Thursday 2/20/2025


________________________________________________________________________
1) The circuit shown in the figure below is in steady-state with switch S open. The
switch is closed at t=0.
a. Find the capacitor voltage vo(0-) just before the switch is closed
and its steady-state value after the switch is closed assuming a
constant source voltage vs.
b. Use the node method to derive a differential equation relating
vo(t) to the source input vs(t) for t0.
c. Find vo (t) and i(t) for t0 assuming a constant sourse voltage vs
and the initial condition you found in (a).
2) Consider the circuit shown in the figure.

a. Obtain a mathematical model for the circuit using the loop method.
b. Define a suitable set of state variables and obtain the state variable model.
c. Use the method of Complex Impedances to determine the total impedance of the
circuit.
d. Determine the transfer function V0/Vs using (c) and either (a) or (b). Show that both
methods give the same result.
e. Use Matlab (or if you prefer Simulink) to numerically find and plot v0(t) and i1(t) for
0t2 in response to a square wave input vs of amplitude 5 V and frequency 10 Hz
(zero initial conditions). Assume R=50 , L=0.1 H, and C=0.001 F.
3) Text Problem 6.26 with the capacitor on the left replaced by inductor L.
4) Solve Text Problem 6.41 if the stall torque TL=1.9 N.m.
5) Consider the robot arm of Text Problem 6.42 and assume that L=0 and the moment of
inertia of the arm about the axis of rotation is Iarm.
a) Drive an expression for the effective inertia felt at the motor shaft in terms of
Ni’s, Iarm, and and IGi’s.
b) Given the numerical values specified in the problem statement find and plot the
motor input voltage, speed, current, and power profile required to produce a
sinusoidal arm motion (t)=0.1 sin t. Assume N1N2=20.

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