ME 375
HOMEWORK #2
Fall 2012
Out: August 29, 2012
Due: September 5, 2012
Problem #1 (30%)
Blocks A and B (each having a mass of m) are connected by the cablepulley system shown. A
constant force fo is applied to block B as shown. Let x represent the posi
Fall 2007  PROBLEM 1: (40%)
Consider the following system. The mass slides without friction, and does not tip. Assume that
the wheel rolls without slipping.
x(t)
B
I, m 2
m1
K
r
!(t),"(t)
R
The overall goal of this problem is to find the equations of mot
ME 375
HOMEWORK #2
Spring 2009
Out: Jan. 20th, 2010
Due: Jan. 27th, 2010
As was the case for HW1, free body diagrams (with coord. systems, internal forces, etc.) and element law
equations clearly indicated for any modeling problem. Also, equations of moti
ME 375 Spring 2013
Homework No. 2
Due: Wednesday, January 23
Problem No. 1 (40%)
PART I
A homogeneous disk (having an outer radius of R and of mass m) is pinned to ground
at its center O. Block B (of mass 2m) is constrained to move along a smooth horizont
ME 375 Spring 2011
Homework No. 1
Due: Friday, January 21
Problem No. 1 (30%)
A system is made up of a homogeneous disk (of mass m and outer radius R) pinned to
ground at O. A cable is wrapped around the outer surface of the disk, with one end of the
cabl
ME 375
HOMEWORK #5
Spring 2010
Out: Feb. 10th, 2010
Due: Feb. 17th, 2010
Problem #1 (30%)
The dynamics of vertical motion of a vehicle can be approximated with a simple 2 mass model, the Quartercar
Model. The model captures the interaction of the suspens
ME 375
HOMEWORK #12
Out: December 3rd, 2010
Fall 2010
Due: December 10th, 2010
PROBLEM 1: (40%)
Sketch the root locus for K 0 in the equation 1 + KL( s ) = 0 and the listed choices for L( s) .
Clearly show your steps in order to receive credits. Also, ana
ME 375
HOMEWORK # 4
Spring 2009
Out: February 4, 2009 Due: February 11, 2009 (at the beginning of class)
PROBLEM 1: (40%) Consider the following set of differential equations that represent an engine supported by elastomeric mounts and excited by a recipr
ME 375: System Modeling and Analysis  Spring 2012
Homework No. 2
Assigned: Wednesday, January 18
Due: Wednesday, January 25
Problem 2.1 (30%)
A stepped pulley (having a mass moment of inertia of I A ) is pinned to ground at its
center of mass A. A second
ME 375: System Modeling and Analysis  Spring 2012
Homework No. 2
Assigned: Wednesday, January 18
Due: Wednesday, January 25
Problem 2.1 (30%)
A stepped pulley (having a mass moment of inertia of I A ) is pinned to ground at its
center of mass A. A second
ME 375 System Modeling and Analysis
Homework 10 Solution
Out: 4 April 2012
Due: 30 11 April 2012
Problem 1:
You are given the following system: G ( s ) =
20
.
s + 12s + 20
2
a) Using Laplace and Inverse Laplace, calculate the unit step response of this sy
ME 375
HOMEWORK #5
Spring 2010
Out: Feb. 10th, 2010
Due: Feb. 17th, 2010
Problem #1 (30%)
The dynamics of vertical motion of a vehicle can be approximated with a simple 2 mass model, the Quartercar
Model. The model captures the interaction of the suspens
+
x
Example 9
We have seen that the EOM for a springmassdashpot
system with the spring and dashpot in PARALLEL is:
k
f(t)
m
!
m! + cx + kx = f ( t )
x
c
+
What is the EOM with the spring and dashpot in
SERIES?
x
f(t)
m
c
k
Example 10
Consider the follow
ME 375: System Modeling and Analysis  Spring 2012
Homework No. 2
Assigned: Wednesday, January 18
Due: Wednesday, January 25
Problem 2.1 (30%)
A stepped pulley (having a mass moment of inertia of I A ) is pinned to ground at its
center of mass A. A second
ME 375
HOMEWORK #3
Fall 2012
Out: September 5, 2012
Due: September 12, 2012
PROBLEM 1: (30%)
a) For u(t) shown below, determine the Laplace transform U(s).
b) If Y ( s)
s3
is the Laplace transform of y(t), what is y(t=0)?
6 s 5s 4
c) If Y ( s)
s3
is the
ME 375 Spring 2013 Due: Wednesday, April 17th Problem No. 1 (30%) Consider the automobile speed control system depicted in the following figure, where R is the desired speed, Y is the actual speed of the car, and W is the road grade (in percent) which rep
!
ME 375
HOMEWORK #2
Spring 2009
Out: Jan. 20th, 2010
Due: Jan. 27th, 2010
As was the case for HW1, free body diagrams (with coord. systems, internal forces, etc.) and element law
equations clearly indicated for any modeling problem. Also, equations of mo
ME 375 Spring 2011
Homework No. 2
Due: Friday, January 28
Problem No. 1 (30%)
Gears 1 and 2 (having masses of m and 2m, respectively) mesh at their common contact
point C (no slip). Flexible shafts having torsional stiffnesses of 2K and K connect gears 1
ME 375
HOMEWORK #10
Fall 2010
Due: November 12th, 2010
Out: November 5th, 2010
PROBLEM 1: (30%)
A schematic of the water level control system in the toilet tank is shown below. After a flush, the water level
decreases as water flows into the toilet bowl.
ME 375
HOMEWORK #8 SOLUTION
Out: March. 10th, 2010
Spring 2010
Due: March 17th, 2010
PROBLEM 1: (30%)
(a) Sketch the complex plane and shade the region for system poles locations corresponding to a damping
ratio greater than 0.75
(b) Sketch the complex pl
ME 375
HOMEWORK #6
Fall 2009
Out: Oct. 7, 2009
Due: Oct. 14, 2009
Problem 1: (50%)
A first order system is subject to an input u,
5y + y = u
a) If u is a unit step input, what is the forced response y(t) of the system (for zero initial conditions)?
b) If
ME375 Handouts
Bode Diagrams (Plots)
Bode Diagrams (Plots)
A unique way of plotting the frequency response function, G(j), w.r.t. frequency of
systems
systems.
Consists of two plots:
Magnitude Plot : plots the magnitude of G(j) in decibels w.r.t. logari
ME 375
HOMEWORK #4
Fall 2012
Out: September 12, 2012
Due: September 19, 2012
Problem #1 (40%)
The transfer function G(s) for a system with input U(s) and output Y (s) has the following
properties:
a static gain of 6
one zero: z1 = 1
two poles: p1 = 2
ME 375 System Modeling and Analysis
Section 9 Block Diagrams and
Feedback Control

G(s)
H(s)
Spring 2009
School of Mechanical Engineering
Douglas E. Adams
Associate Professor
9.1
Key Points to Remember
Block diagrams
Each block is completely independent
ME 375 System Modeling and Analysis
Section 1 Introduction
+

3
+

1
2
Spring 2009
School of Mechanical Engineering
Douglas E. Adams
Associate Professor
1
1.1
What We Will Do
Example: vehicle speed control
MODEL:
Solid mechanics, dynamics, circuits, hea