Mechanical Vibration Assignmnet No 1

Assignments No – I

Date of Issue: 8^th August, 2013                                             Date of Submission: 14^th August, 2013

1.      Represent the periodic motion given in figure 1 by harmonic motion

Figure 1

2.      Find the sum of harmonic motion of equal amplitude but of slightly different frequencies. Discuss the beat phenomenon that results from this sum.

3.      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.

4.      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.

5.      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?

6.      A simple U tube manometer filled with liquid is ahown in figure 2. Calculate the frequency of resulting motion if the minimum length of a manometer tube is 0.15m.

Figure2

7.      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

8.      A vibratory system is defined by the following parameters:

m = 3kg, k = 100 N/m, C = 3 N- sec/m. Determine

a.      The damping factor

b.      The natural frequency of the damped vibration

c.       The logarithmic decrement

d.      The ratio of two consecutive amplitudes

The number of cycles after which the original amplitude is reduced to 20 percent.

Note: On the last date of submission of your assignment, a minor test of 20 marks will be conducted