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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
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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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: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
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
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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