SYSTEM DYNAMICS CONNECT
3rd Edition
ISBN: 9781264201730
Author: Palm
Publisher: MCG CUSTOM
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Chapter 6, Problem 6.3P
The Wheatstone bridge, like that shown in Figure P6.3, is used for various measurements. For example, a strain gage sensor utilizes the fact that the resistance of wire changes when deformed. If the sensor is one resistance leg of the bridge, then the deformation can be determined from the voltage
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A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below.
From the free body diagram, the ordinary differential equation of the vehicle is:
m * dv(t)/ dt + bv(t) = u (t)
Where:
v (m/s) is the velocity of the vehicle,
b [Ns/m] is the damping coefficient,
m [kg] is the vehicle mass,
u [N] is the engine force.
Question:
Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system):
1. What is the order of this system?
A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below.
From the free body diagram, the ordinary differential equation of the vehicle is:
m * dv(t)/ dt + bv(t) = u (t)
Where:
v (m/s) is the velocity of the vehicle,
b [Ns/m] is the damping coefficient,
m [kg] is the vehicle mass,
u [N] is the engine force.
Question:
Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system):
A. Use Laplace transform of the differential equation to determine the transfer function of the system.
A mass of 2 kilograms is on a spring with spring constant k newtons per meter with no damping. Suppose the system is at rest and at time t = 0 the mass is kicked and starts traveling at 2 meters per second. How large does k have to be to so that the mass does not go further than 3 meters from the rest position?
use 2nd order differential equations to solve (mechanical vibrations)
Chapter 6 Solutions
SYSTEM DYNAMICS CONNECT
Ch. 6 - Prob. 6.1PCh. 6 - Determine the voltage v1 in terms of the supply...Ch. 6 - The Wheatstone bridge, like that shown in Figure...Ch. 6 - Prob. 6.4PCh. 6 - Obtain the model of the voltage v1 , given the...Ch. 6 - Prob. 6.6PCh. 6 - Prob. 6.7PCh. 6 - Prob. 6.8PCh. 6 - Prob. 6.9PCh. 6 - The resistance of a telegraph line is R=10 , and...
Ch. 6 - Obtain the model of the voltage vo , given the...Ch. 6 - Obtain the model of the voltage vo , given the...Ch. 6 - Obtain the model of the current i, given the...Ch. 6 - Prob. 6.14PCh. 6 - Obtain the model of the currents i1 , i2 , and i3...Ch. 6 - Obtain the model of the currents i1 , i2 , and the...Ch. 6 - Prob. 6.17PCh. 6 - Prob. 6.18PCh. 6 - Prob. 6.19PCh. 6 - Prob. 6.20PCh. 6 - Use the impedance method to obtain the transfer...Ch. 6 - Use the impedance method to obtain the transfer...Ch. 6 - Use the impedance method to obtain the transfer...Ch. 6 - Use the impedance method to obtain the transfer...Ch. 6 - 6.25 Use the impedance method to obtain the...Ch. 6 - Prob. 6.26PCh. 6 - Prob. 6.27PCh. 6 - Prob. 6.28PCh. 6 - Prob. 6.29PCh. 6 - Prob. 6.30PCh. 6 - Prob. 6.31PCh. 6 - Prob. 6.32PCh. 6 - Prob. 6.33PCh. 6 - (a) Obtain the transfer function s/Vi for the...Ch. 6 - (a) Obtain the transfer function s/VLs for the...Ch. 6 - Prob. 6.36PCh. 6 - Prob. 6.37PCh. 6 - Figure P6.38 is the circuit diagram of a...Ch. 6 - Prob. 6.39PCh. 6 - Prob. 6.40PCh. 6 - Prob. 6.41PCh. 6 - Prob. 6.42PCh. 6 - A single link of a robot arm is shown in Figure...Ch. 6 - A conveyor drive system to produce translation of...Ch. 6 - Prob. 6.45PCh. 6 - Prob. 6.46PCh. 6 - Prob. 6.47P
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