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Q 2(a) Consider the rotating system in Figure 2. Treat the two shafts as ideal torsional springs with stiffness k, and k, as shown. The angular position of the lumped mass with moment of inertia j is 8,, and the angular position of the free end of the shaft, supported by a viscous bearing with damping factor B, is 62. Derive a suitable state-variable model for the system. 1.e k, k, Figure 2 Q 2(b) Consider a two-metre long horizontal uniform rod that is fixed at both ends. The properties of the rod are such that E 40 + where L is the number formed by the last two digits of your student number. For example, if your student number ends in 97, then = (40 +) = 88.52 = 7832.25 Include your value of from the start in your work. The fixed end at x = 0, because of vibration in the support, is oscillating horizontally with an amplitude of 4 mm and with a frequency w rad/s. Starting from the equation for longitudinal vibrations in a rod, find a formula for the vibration amplitude along the rod in terms of w. Q 2(c) The horizontal position of the mass M in Figure 3, x1(t), measured to the right from its equilibrium position, is controlled by an extemal system not shown in the diagram. A state-variable equation should not include any derivatives on its right-hand side. Find state-variable equations for the system (indicating clearly what any state- variables are and how they are measured). Include any free body diagrams required.

Q 2(a) Consider the rotating system in Figure 2. Treat the two shafts as ideal torsional springs with stiffness k, and k, as shown. The angular position of the lumped mass with moment of inertia j is 8,, and the angular position of the free end of the shaft, supported by a viscous bearing with damping factor B, is 62. Derive a suitable state-variable model for the system. 1.e k, k, Figure 2 Q 2(b) Consider a two-metre long horizontal uniform rod that is fixed at both ends. The properties of the rod are such that E 40 + where L is the number formed by the last two digits of your student number. For example, if your student number ends in 97, then = (40 +) = 88.52 = 7832.25 Include your value of from the start in your work. The fixed end at x = 0, because of vibration in the support, is oscillating horizontally with an amplitude of 4 mm and with a frequency w rad/s. Starting from the equation for longitudinal vibrations in a rod, find a formula for the vibration amplitude along the rod in terms of w. Q 2(c) The horizontal position of the mass M in Figure 3, x1(t), measured to the right from its equilibrium position, is controlled by an extemal system not shown in the diagram. A state-variable equation should not include any derivatives on its right-hand side. Find state-variable equations for the system (indicating clearly what any state- variables are and how they are measured). Include any free body diagrams required.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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M Figure 3
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Q 2(a) Consider the rotating system in Figure 2. Treat the two shafts as ideal torsional springs with stiffness k, and ką as shown. The angular position of the lumped mass with moment of inertia j is 8, and the angular position of the free end of the shaft, supported by a viscous bearing with damping factor B, is e2. Derive a suitable state-variable model for the system. k, k, B Figure 2 Q 2(b) Consider a two-metre long horizontal uniform rod that is fixed at both ends. The properties of the rod are such that E 2 m2 40 + where L is the number formed by the last two digits of your student number. For example, if your student number ends in 97, then = (40 +7) = 88.5? = 7832.25 . Include your value of from the start in your work. The fixed end at x = 0, because of vibration in the support, is oscillating horizontally with an amplitude of 4 mm and with a frequency w rad/s. Starting from the equation for longitudinal vibrations in a rod, find a formula for the vibration amplitude along the rod in terms of w. Q 2(c) The horizontal position of the mass M in Figure 3, x1(t), measured to the right from its equilibrium position, is controlled by an external system not shown in the diagram. A state-variable equation should not include any derivatives on its right-hand side. Find state-variable equations for the system (indicating clearly what any state- variables are and how they are measured). Include any free body diagrams required.
Transcribed Image Text:Q 2(a) Consider the rotating system in Figure 2. Treat the two shafts as ideal torsional springs with stiffness k, and ką as shown. The angular position of the lumped mass with moment of inertia j is 8, and the angular position of the free end of the shaft, supported by a viscous bearing with damping factor B, is e2. Derive a suitable state-variable model for the system. k, k, B Figure 2 Q 2(b) Consider a two-metre long horizontal uniform rod that is fixed at both ends. The properties of the rod are such that E 2 m2 40 + where L is the number formed by the last two digits of your student number. For example, if your student number ends in 97, then = (40 +7) = 88.5? = 7832.25 . Include your value of from the start in your work. The fixed end at x = 0, because of vibration in the support, is oscillating horizontally with an amplitude of 4 mm and with a frequency w rad/s. Starting from the equation for longitudinal vibrations in a rod, find a formula for the vibration amplitude along the rod in terms of w. Q 2(c) The horizontal position of the mass M in Figure 3, x1(t), measured to the right from its equilibrium position, is controlled by an external system not shown in the diagram. A state-variable equation should not include any derivatives on its right-hand side. Find state-variable equations for the system (indicating clearly what any state- variables are and how they are measured). Include any free body diagrams required.
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