This document contains 18 problems related to dynamics of machines and vibration analysis. The problems cover topics such as determining natural frequency of vibration, calculating damping force and amplitude for damped harmonic motion, finding transmissibility ratio and force transmitted for machines supported on springs, analyzing forced vibration with damping, and vibration isolation. Solutions require use of concepts like damping coefficient, stiffness, damping factor, amplitude, phase angle, and transmissibility.

1. ME8594 - DYNAMICS OF MACHINES
UNIT –IV (Part –B)
Prepared By: N. E. Godwin Pithalis Page 1
1. A body having a mass of 15 kg is suspended from a spring which deflects 12 mm under weight of the mass.
Determine the frequency of the free vibrations. What is the viscous damping force needed to make the motion a
periodic at a speed of 1 mm/s? If, when damped to this extent, disturbing force having a maximum value of 100
N and vibrating at 6 Hz is made to act on the body, determine the amplitude of the ultimate motion.
(DEC-2010)
2. A machine supported symmetrically on four springs has a mass of 80 kg. The mass of the reciprocating parts
is 2.2 kg which move through a vertical stroke of 100 mm with simple harmonic motion. Neglecting damping,
determine the combined stiffness of the springs so that the force transmitted to the foundation is 1/20th of the
impressed force. The machine crankshaft rotates at 800 rpm. If, under actual working conditions, the damping
reduces the amplitudes of successive vibrations by 30%, find: (i) the force transmitted to the foundation at 800
rpm, and (ii) the force transmitted to the foundation at resonance.
(DEC-2009, 2010)
3. A vibratory body of mass 150 kg supported on springs of total stiffness 1050 Kn/m has a rotating unbalance
force of 525 N at a speed of 6000 rpm. If the damping factor is 0.3, determine (i) the amplitude caused by the
unbalance and its phase angle (ii) the transmissibility and (iii) the actual force transmitted and its phase angle
(DEC-2012)
4. What do you understand by transmissibility? Describe the method of finding the transmissibility ratio from
unbalanced machine supported with foundation (DEC-2012)
5. (i) Derive the relation for the displacement of mass from the equilibrium position of a damped vibration
system with harmonic forcing (DEC-2013) 12
(ii) Define the term vibration isolation (DEC-2013) 4
6. (i) Discuss the forcing due to support motion (DEC-2013)10
(ii) What is meant by magnification factor in case of forced vibration? (DEC-2013) 6
7. A machine part having a mass of 2.5 Kg vibrates in a viscous medium. A harmonic exciting force of 30 N
acts on the part and causes resonant amplitude of 14 mm with a period of 0.22 sec .Find the damping coefficient
.If the frequency of the exciting force is charged to 4 Hz, determine the increase in the amplitude of the forced
vibrations upon the removal of damper. (MAY-2008)
8. The following data relate to a machine supported on four springs. Mass of machine = 120 Kg, Stroke length =
90 mm, Mass of reciprocating parts = 2.5 Kg, Speed =750 rpm. Springs are symmetrically placed with respect
to the center of mass of the machine .Neglecting damping; find the combined stiffness of springs so that the
force transmitted to the foundation is 1/22 of the impressed force. If under actual working conditions, the
damping reduces the amplitude of the successive vibrations by 25 %, determine the force transmitted to the
foundation at 750 rpm and at resonance. Also find the amplitude of vibrations at resonance.
(MAY-2008)

2. ME6505 - DYNAMICS OF MACHINES
UNIT –IV (Part –B)
Prepared By: N. E. Godwin Pithalis Page 2
9. (i) Establish an expression for the amplitude of forced vibration 8 (MAY-2014)
(ii) What do you understand by vibration isolation and transmissibility, Explain with suitable example
(MAY-2014) 8
10. A mass of 10kg is suspended from one end of a helical spring, the other end being fixed. The
stiffness of the spring is 10 N/mm. The viscous damping causes the amplitude to decreases to one-
tenth of the initial value in four complete oscillations. If a periodic force of 150cos50t N is applied at
the mass in the vertical direction .Find the amplitude of the forced vibrations? What is its value of
resonance? (MAY-2013, 2014, DEC-2014)
11. A machine of 100 kg is supported on a spring of stiffness 700KN/m and has an unbalanced
rotating element, which results in a disturbing force of 350 N at a speed of 3000 rpm. Assuming a
damping factor of 0.2, determine its amplitude of motion due to unbalance, the transmissibility, and
the transmitted force. (DEC-2011)
12. A machine of mass 1000kg is acted upon by an external force of 2450 N at a frequency of 1500 rpm. To
reduce the effects of vibration, isolator of rubber having state deflection of 2mm under the machine load and an
estimated damping of 0.2 are used. Determine the force transmitted to the foundation, the amplitude of vibration
and the phase lag. (DEC-2011)
13. An electric motor is supported on a spring and a dashpot. The spring has the stiffness 6400N/m and the
dashpot offers resistance of 500 N at 4 m/sec. The unbalanced mass 0.5 kg rotates at 5 cm radius and the total
mass of vibratory system is 20 kg. The motor runs at 400 rpm. Determine damping factor, amplitude of
vibration and phase angle, resonant speed and resonant amplitude and forces exerted by the spring and dashpot
on the motor. (MAY-2011, 2012)
14. A vehicle weighs 490 kg and total spring constant of its suspension system is 300 N/cm. The
profile of the road is approximated as SHM of amplitude 4 cm and wavelength of 4m. Determine the
critical speed of the vehicle, the amplitude of the steady state motion of the mass when the vehicle is
driven at critical speed when the damping factor is 0.5 and amplitude of the steady state motion when
the vehicle is driven at 57 km/hr with same damping factor. (MAY-2011)
15. A vibrating body is supported by six isolators each having stiffness of 32000 N/m and six dashpots having
damping factor as 400 N-sec/m. The vibrating body is to be isolated by a rotating device having amplitude of
0.06 mm at 600 rpm. Take m = 30 kg. Determine the amplitude of vibration of the body and dynamic load on
each isolator due to vibration. (MAY-2012)
16. A harmonic exiting force of 25N is acting on a machine part, which is having a mass of 2Kg and is
vibrating in viscous medium. The exciting force causes resonant amplitude of 12.5mm with a period of
0.2sec. Determine the damping coefficient. If the system is excited by a harmonic force of frequency 4
Hz, find the increase in amplitude of forced vibration when damper is removed.
(DEC-2009)

3. ME6505 - DYNAMICS OF MACHINES
UNIT –IV (Part –B)
Prepared By: N. E. Godwin Pithalis Page 3
17. The mass of an electric motor is 120 kg and it runs at 1500 rpm. The armature mass is 35 kg and its
centre of gravity lies 0.5mm from axis of rotation. The motor is mounted on five springs of negligible
damping. So that the force transmitted is one-eleventh of the impressed force. Assume that the mass of
the motor is equally distributed among the five springs. Determine (i) the stiffness of each spring (ii)
the dynamic force transmitted to the base at the operating speed. (iii) Natural frequency of system.
(MAY-2013)
18. A machine Part of mass 2 kg vibrates in a viscous medium. Determine the damping coefficient when a
harmonic exiting force of 35 N results in resonant amplitude of 12.5 mm with a period of 0.2 sec. If the system
is excited by a harmonic force of frequency 4Hz, what will be the percentage increase in the amplitude of
vibration when damper is removed as compared with that with damping? (DEC-2014)