Lecture 25
Homework
Problem 25.1
The uniform bar has a length L a mass m1 a centroidal moment of inertia JG and is supported by
two springs of stiffness k. The mass m2 is hung from the bar by means of another spring, k2, and
is subjected to the force F(t) as shown.
a) Assuming small angles, and using the coordinates shown below, determine the
differential equations of motion of the system using Lagrange’s equations. Write the
equations in 2nd order matrix form.
b) If k = 1000 N/m, k2 = 1500 N/m, L = 0.5 m, e = 0.1 m, m1 = 0.5 kg, and m2 = 0.4 kg
determine the natural frequencies and natural modes. Report the modes in three different
ways 1) the modes directly from Matlab, 2) the modes normalized so that x2 = 1, and 3)
unit normalized modes, that is, the magnitudes of the eigenvectors are one.
e
k
k
k2
G
θ
x1
x2
F(t)
m2
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