5 Problem Consider the single degree-of-freedom rotational system shown below with two masses m con- centrated at each end. An upward force, u(t), is applied at the leftmost point, and two springs with stiffness k are attached at distances away from the center rotation point O. The springs are unstretched when the angle of the rod is = 0. Assume small angles and account for weight of masses. • Derive an expression for the natural frequency in terms of the parameters given. Show that the transfer function for this system is Ⓒ(s) U(s) -2 4mLs2+kL
5 Problem Consider the single degree-of-freedom rotational system shown below with two masses m con- centrated at each end. An upward force, u(t), is applied at the leftmost point, and two springs with stiffness k are attached at distances away from the center rotation point O. The springs are unstretched when the angle of the rod is = 0. Assume small angles and account for weight of masses. • Derive an expression for the natural frequency in terms of the parameters given. Show that the transfer function for this system is Ⓒ(s) U(s) -2 4mLs2+kL
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:5 Problem
Consider the single degree-of-freedom rotational system shown below with two masses m con-
centrated at each end. An upward force, u(t), is applied at the leftmost point, and two springs
with stiffness k are attached at distances away from the center rotation point O. The springs are
unstretched when the angle of the rod is 0 = 0. Assume small angles and account for weight of
masses.
• Derive an expression for the natural frequency in terms of the parameters given.
• Show that the transfer function for this system is
Ⓒ(s)
U(s)
-2
4mLs²+kL

Transcribed Image Text:m
L/2
Tu(t) j
L/2
k
L/2
Hint: Recall that for N masses, the inertia around point O is:
N
Io = Σmil|ri/o||²
i=1
L/2
k
where ri/o is the vector that points to the ith mass from point O.
0
m
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