CTIEMT, SHAHPUR
MECHANICAL
ENGINEERING DEPARTMENT
MECHANICAL VIBRATION
Assignment No # 1
Date of Issue: 28th
Jan, 2013 Date of Submission: 4th
Feb, 2013
1. Represent the periodic
motion given in figure 1 by harmonic motion
Figure 1
2. Represent the periodic
motions given in figure 2 by harmonic motion.
Figure 2
3. Find the sum of harmonic
motion of equal amplitude but of slightly different frequencies. Discuss the
beat phenomenon that results from this sum.
4. Split up the harmonic
motion 8 sin (ωt + π/4) into two harmonic motions one of which has amplitude of
10 and phase difference zero.
5. A steel shaft 6 cm
diameter and 50 cm long fixed at one end carries a flywheel of weight of 1000
kgf and radius of gyration 30cm at its free end. Find the frequency of free
longitudinal transverse and torsional vibration E= 2 x 106 kgf/ cm2,
C = 3.8 x 106 kgf/ cm2.
6. A shock absorber is to
be designed so that its overshoot is 10% of the initial displacement when
released. Determine the damping factor. If the damping factor is reduced to one
half this values, what will be the overshoot?
7. Why do
we consider natural frequency in vibration?
8. A simple U tube
manometer filled with liquid is ahown in figure 3. Calculate the frequency of
resulting motion if the minimum length of a manometer tube is 0.15m.
Figure 3
9. A gun barrel having mass
560kg is designed with the following data: Initial recoil velocity 36 m/sec,
recoil distance on firing 1.5 m
Calculate:
(a) Spring constant
(b) Damping coefficient
(c) Time required for the
barrel to return to a position 0.12 m from its initial position