a. Derive the differential equations of motion and obtain the mass and stiffness matrices. b. Caleulate the natural frequencies and the mode shapes.

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
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MECHANICAL VIBRATIONS TWO DEGREE OF FREEDOM

P4.2 Consider the system in Figure P4.2.
Massless
and
rigid bar
2m
Зт
2k
Figure P4.2 Massless rigid bar with masses lumped at ends and supported on springs
232
Vibration of Mechanical Systems
a. Derive the differential equations of motion and obtain the
mass
and stiffness matrices.
b. Calculate the natural frequencies and the mode shapes.
c. Find the initial conditions such that the free vibration is sinusoidal
with each natural frequency.
Transcribed Image Text:P4.2 Consider the system in Figure P4.2. Massless and rigid bar 2m Зт 2k Figure P4.2 Massless rigid bar with masses lumped at ends and supported on springs 232 Vibration of Mechanical Systems a. Derive the differential equations of motion and obtain the mass and stiffness matrices. b. Calculate the natural frequencies and the mode shapes. c. Find the initial conditions such that the free vibration is sinusoidal with each natural frequency.
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