Mechanical Vibrations
ME 429
Lecture – 4
(Solved Problems)
Dr. Elwaleed Awad Khidir & Dr. Syed Yousufuddin
Problem-1
Derive the equation of motion of the system shown in Fig. 1, using the following
methods:
(a) Newton s second law of motion, and
(b) principle of conservation of energy.
Figure 1
Problem-1
(a)
(b)
Problem-2
The 7-kg disk is pin-connected at its midpoint (Figure 2). Determine the natural
period of vibration of the disk if the spring have sufficient tension in them to prevent
the cord from slipping on the disk as it oscillates.
600mm
k = 600 N/m
k = 600 N/m
Figure 2
Problem-3
Figure 3 shows a homogeneous cylinder of radius R and mass m that is free to rotate
about its axis of rotation and that is connected to the wall through a spring. Assuming
that the cylinder rolls on a rough surface without sliding, obtain the kinetic energy
and potential energy of the system. Then derive the equations of motion from the fact
that the total energy is constant. Assume that x and θ are measured from respective
equilibrium positions.
Figure 3
Problem-3
Problem-3
Problem-4
Derive the equation of motion for the system shown in Figure 4 and find the natural
frequency for the system
k
r
Pulley , mass moment of
inertia JO
m
Figure 4
Problem-5
Derive the equation of motion of the system shown in Fig. 5 using Newton s second
law of motion,
Figure 5
Problem-5
Problem-6
Derive the equation of motion for the system shown in Figure 6 and find the natural
frequency for the system
k
4r
r
Pulley , mass moment of
inertia JO
m
Figure 6
Problem-7
Problem-8