Assiut University
MDP 0515-Mechanical Vibrations
Faculty of Engineering
Dr. Yasser Abdelrhman
Mechatronics and Robotics Program
yasser_hmj@yahoo.com
Sheet no. 1: Fundamentals of Mechanical Vibrations - SOLUTION
1. Give two examples each of the bad and the good effects of vibration.
Good Effects: 1. Hearing 2. Vibration tester 3. Washing Machine 4. Drills.
Bad effects: 1. Resonance 2. Vibration in machinery 3. Noise.
2. How are τ, ω, and f related to each other?
τ=1/f, ω=2π f
3. Define the number of degrees of freedom of a vibrating system.
4. How do you connect several springs to increase the overall stiffness?
Connecting them in parallel
5. Define these terms:
Cycle, amplitude, period, and natural frequency.
Cycle: The motion completed during the period. The movement of a vibrating body from
its undisturbed or equilibrium position to its extreme position in one direction, then to the
equilibrium position, then to its extreme position in the other direction, and back to
equilibrium position
Amplitude: The maximum displacement of a vibrating body from its equilibrium position
Period: the time to complete one cycle
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6. Choose the correct answer from the following:
i. When a system vibrates in a fluid medium, the damping is
(a) Viscous
(b) Coulomb
ii.
When parts of a vibrating system slide on a dry surface, the damping is
(a) Viscous
(b) Coulomb
(c) solid
(c) solid
iii.
When the stress-strain curve of the material of a vibrating system exhibits a hysteresis
loop, the damping is
(a) Viscous
(b) Coulomb
(c) solid
iv.
The number of degrees of freedom of a simple pendulum is:
(a) 0
(b) 1
(c) 2
The equivalent spring constant of two series springs with stiffnesses k1 and k2 is
v.
7.
8.
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9. Determine the equivalent spring constant of the system shown
10.
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11..
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12.A 0.45 kg mass attached to a light spring elongates it 0.79 cm. Determine the natural
frequency of the system.
13. What mass attached to the spring of Prob. 12 would result in natural frequency of 100
cycles per minute?
14. In a spring-mass system k1, m has a natural frequency of f1. If a second spring k2 is added
in series with the first spring, the natural frequency is lowered to 0.5 f 1 Determine k2 in
terms of k1
15..
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16.A 4.5kg mass, attached to the lower end of a spring whose upper end is fixed, vibrates with
a natural period of 0.45 sec. Determine the natural period when a 2.27 kg. Mass is attached
to the mid-point of the same spring with the upper and lower ends fixed.
17.An unknown mass m kg attached to the end of an unknown spring k has a natural frequency
of 94 c.p.m. when a 0.45kg mass added to m, the natural frequency is lowered to 16.7 c.p.m.
Determine the unknown mass m kg., and the spring constant k N/m.
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