MEL417

Assignment-2

1. The natural frequency of vibration of a person is found to be 5.2 Hz while standing on a

horizontal floor. Assuming damping to be negligible, determine the following:

a. If the weight of the person is 70 Kg, determine the equivalent stiffness of his body in the

vertical direction.

b. If the floor is subjected to a vertical harmonic vibration of frequency of 5.3 Hz and

amplitude of 0.1 m due to an unbalanced rotating machine operating on the floor, determine

the vertical displacement of the person.

2. A hollow steel shaft, of length 100 cm, outer diameter 4 cm, and inner diameter 3.5 cm,

carries the rotor of a turbine, weighing 500 N, at the middle and is supported at the ends in

bearings. The clearance between the rotor and the stator is 0.5 cm The rotor has an

eccentricity equivalent to a weight of 0.5 N at a radius of 2 cm. A limit switch is installed to

stop the rotor whenever the rotor touches the stator. If the rotor operates at resonance, how

long will it take to activate the limit switch? Assume the initial displacement and velocity of

the rotor perpendicular to the shaft to be zero.

3. A spring-mass-damper system is subjected to a harmonic force. The amplitude is found to

be 20 mm at resonance and 10 mm at a frequency 0.75 times the resonant frequency. Find the

damping ratio of the system.

4. A video camera, of mass 2.0 kg, is mounted on the top of a bank building for surveillance.

The video camera is fixed at one end of a tubular aluminum rod whose other end is fixed to

the building as shown in Fig. below. The wind-induced force acting on the video camera,

f(t), is found to be harmonic with 25cos75.3984t N. Determine the cross-sectional dimensions

of the aluminum tube if the maximum amplitude of vibration of the video camera is to be

limited to 0.005 m.

Fig.1

5. A spring-mass system with mass 25Kg and k=10kN/m vibrates on a horizontal surface with

coefficient of friction µ=.3. Under a harmonic force of frequency 8 Hz, the steady state vibration of

the mass is found to be 0.2 m. Determine the equivalent viscous-damping constant of the system.

6. A spring-mass system is subjected to Coulomb damping. When a harmonic force of amplitude 120

N and frequency 2.51 Hz is applied, the system is found to oscillate with an amplitude of 75 mm.

Determine the coefficient of dry friction if m=2kg and k=2100N/m.

7. A spring-mass system consists of a mass weighing 100 N and a spring with a stiffness of 2000

N/m. The mass is subjected to resonance by a harmonic force

Find the amplitude of the forced motion at the end of (a) 1/4cycle, (b) 5/2 cycles, and (c) 23/4 cycles.