ME 563 Fall 2014
Homework Problem 10.1
SOLUTION
Consider the stepped shaft shown below. In the subdomain 0 < x < L / 2 the material
has a shear modulus of G, a mass density of and the cross section has a polar area
moment of 4J. In the subdomain L / 2 < x
ME 563 Fall 2014 SCH/77 OK/
Homework Problem 3. 1'
The thin homogeneous bar shown has a length of L and mass of m. A spring is attached
to end A of the bar, with the other end of the spring able to slide in a smooth horizontal
slot. Note that having the s
ME 563 Fall 2014
Midterm Examination
Problem 1
SOLUTION
A homogeneous wheel (of mass m and outer radius r) is able to roll without slipping on
wedge A. Wedge A is allowed to translate along a smooth guide. A spring of stiffness k
is attached between A and
ME 563 Fall 2014
Homework Problem 4.1
SOLUTION
The two-DOF system shown is described by the coordinates x and . The block and bar
each have a mass of m. The thin bar is homogeneous in its mass distribution and has a
length of L. Let g / L = 2k / m .
a) De
ME 563 Fall 2014
Final Exam Statistics and Solution
Shown below is a listing of the 62 final exam scores (%) for ME 563, along with
the final exam statistics of:
Final exam median score: 84%
Final exam average (mean): 78.7%
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ME 563 Fall 2014
Homework Problem 2.1
SOLUTION
A homogeneous disk of mass m and outer radius R is able to roll without slipping on an
inclined ramp. A spring (of stiffness k) and a dashpot (of damping constant c) connect the
center of the disk O to ground
ME 563 Fall 2014
Homework Problem 6.1
SOLUTION
Consider the three continuous systems shown below. For each system, DERIVE the
boundary conditions at both x = 0 and x = L. Your derivations must include appropriate
free body diagrams in order to receive cre
ME 563 Fall 2014
Homework Problem 9.1
SOLUTION
An automobile moves along a wavy roadway with a constant speed, where the surface of
the roadway is idealized by y(z) = y0 sin2 z / L . The single-DOF model below is to be
used to represent the vertical motio
ME 563 Fall 2014
Homework Problem 8.1
SOLUTION
Consider the T-periodic function f(t) shown below.
a) Determine the Fourier series of f(t). Take advantage of any symmetry/antisymmetry/zero mean value characteristics of f(t) when finding the Fourier series
ME 563 Fall 2014
Homework Problem 1.1
SOLUTION
Consider the three-degree-of-freedom system shown below made up of three particles A,
B and C, each of mass m, with the system moving within a horizontal plane. Let x1
describe the absolute motion of particle
ME 563 Fall 2014
Homework Problem 7.1
SOLUTION
Consider the single-DOF model of an automotive system shown below as the
automobile moves along a wavy-surfaced roadway with a constant speed of v. The
profile of the roadway is given by y(z) = y0 sin( z / L)
ME 563 Fan 2014 Wad
Homework Problem 5.1
Consider the two-DOF system shown below whose motion is to be described by the
absolute generalized coordinates x1 and x2.
a) Determine the natural frequencies and modal vectors for the system.
b) Determine the bea