Aerospace and Mechanical Engineering

Homework 6

B. Goodwine J. Lucey Fall, 2003 |
Issued: October 12, 2003 Due: October 15, 2003 (US) 16 October 2003 (UK) |

- Consider the system in the following figure where ,
, and .
Find

- the extension of the spring due to the suspended weight;
- the static displacement of the spring due to the maximum applied force; and,
- the amplitude of the forced motion of the weight.

- A spring-mass system like the one in the previous problem
consists of a mass weighting and a spring with stiffness . The mass is subjected to resonance by a harmonic force
. Find the amplitude of the forced motion
at the end of
- cycle;
- cycles; and,
- cycles.

- Considering the system in the previous figure, assume that , , and . If
, plot
the response of the system for to . Explain the
results.
- Find the frequency ratio
at which
the amplitude of a single degree of freedom damped system illustrated
in the following figure attains the
maximum value. Also find the value of the maximum amplitude.
- For a vibrating system where , and , a harmonic force of amplitude and a frequency of
acts on the mass. If the initial displacement and velocity
of the mass are and , find the complete solution
representing the motion of the mass.
- An automobile is modeled as a single degree of freedom system
vibrating in the vertical direction. It is driven along a road whose
elevation varies sinusoidally. The distance from peak to trough is
and the distance along the road between the peaks is .
If the natural frequency of the automobile is and the dam;ping
ratio of the shock absorbers is , determine the amplitude of
vibration of the automobile at a speed of . Also find the
speed at which the ride would be most unfavorable for the passengers.
- Consider the single degree of freedom building structure
illustrated in the following figure.
Find the horizontal displacement of the floor (the mass ) of the building frame where the ground

*acceleration*is given by . Let , , and . - A spring mass system is subjected to Coulomb damping. When a harmonic force of amplitude and frequency of is applied, the system is found to oscillate with an amplitude of . Determine the coefficient of dry friction if and .

B. Goodwine (

J. Lucey (