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Q 2(b) Consider the non-uniform beam shown in Figure 3. It's horizontal when in equilibrium. Its mass is m kg and its moment of inertia about its mass centre, G, is kg - m². Assuming any horizontal motion is negligible, write equations of motion for the system and find its mass and stiffness matrices. 0.5 m 1m 2k Figure 3

Q 2(b) Consider the non-uniform beam shown in Figure 3. It's horizontal when in equilibrium. Its mass is m kg and its moment of inertia about its mass centre, G, is kg - m². Assuming any horizontal motion is negligible, write equations of motion for the system and find its mass and stiffness matrices. 0.5 m 1m 2k Figure 3

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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Q 2(a) Consider the system shown in Figure 2. There is damping between the two masses with coefficient c. Both positions indicated in the diagram are measured from the equilibrium positions. The position of the upper mass, x2(t), is controlled over time. Find suitable state-variable equations for the system that don't include differential terms on their right-hand sides. Write an output equation for the force, fa(t), that must be applied to the right on the upper mass to make it move in the desired manner. Briefly, give one reason why it's best to avoid having derivatives of inputs in state- variable equations. m, XXXXXXX C k, m, Figure 2 Q 2(b) Consider the non-uniform beam shown in Figure 3. It's horizontal when in equilibrium. Its mass is m kg and its moment of inertia about its mass centre, G, is * kg - m2. Assuming any horizontal motion is negligible, write equations of motion for the system and find its mass and stiffness matrices. 1m 0.5 m 2k Figure 3 Q 2(c) Consider the system in Q2(b). Its properties are m = 2 and k = 100 N/m. An upwards force f = 100 sin 200t N is applied to the beam at a point 0.2 m to the right of G. Find the resulting amplitude of vibration of the beam as a function of x, where x is measured to the right from G. Also, find the point on the beam with the lowest vibration amplitude, and the vibration amplitude at that point.
Transcribed Image Text:Q 2(a) Consider the system shown in Figure 2. There is damping between the two masses with coefficient c. Both positions indicated in the diagram are measured from the equilibrium positions. The position of the upper mass, x2(t), is controlled over time. Find suitable state-variable equations for the system that don't include differential terms on their right-hand sides. Write an output equation for the force, fa(t), that must be applied to the right on the upper mass to make it move in the desired manner. Briefly, give one reason why it's best to avoid having derivatives of inputs in state- variable equations. m, XXXXXXX C k, m, Figure 2 Q 2(b) Consider the non-uniform beam shown in Figure 3. It's horizontal when in equilibrium. Its mass is m kg and its moment of inertia about its mass centre, G, is * kg - m2. Assuming any horizontal motion is negligible, write equations of motion for the system and find its mass and stiffness matrices. 1m 0.5 m 2k Figure 3 Q 2(c) Consider the system in Q2(b). Its properties are m = 2 and k = 100 N/m. An upwards force f = 100 sin 200t N is applied to the beam at a point 0.2 m to the right of G. Find the resulting amplitude of vibration of the beam as a function of x, where x is measured to the right from G. Also, find the point on the beam with the lowest vibration amplitude, and the vibration amplitude at that point.
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