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Figure Q4 shows the schematic for a pressure pad. The pad has area A and is connected to a rod of length 6L which is free to rotate about its hinge point at 0. The rod is supported by a damper of coefficient c and a spring with stiffness k, in the positions shown. The rod has a moment of inertia 1, about an axis through the pivot point, 0. The pad has a pressure P(t) applied to it which causes an angular displacement, 0, as indicated. Assuming small angular displacements, derive an expression for the transfer function of the system relating angular displacement 0 to an input pressure P. Derive an expression for the displacement of the rod, 0(t), in response to a step input of pressure of magnitude 100 Pa given the following data: 1, = 4 kgm²; c = 40 Ns/m; k= 500 N/m; L= 0.5 m; A= 0.2 m² Working from first principles, calculate the rise time, t,, of the system.

Figure Q4 shows the schematic for a pressure pad. The pad has area A and is connected to a rod of length 6L which is free to rotate about its hinge point at 0. The rod is supported by a damper of coefficient c and a spring with stiffness k, in the positions shown. The rod has a moment of inertia 1, about an axis through the pivot point, 0. The pad has a pressure P(t) applied to it which causes an angular displacement, 0, as indicated. Assuming small angular displacements, derive an expression for the transfer function of the system relating angular displacement 0 to an input pressure P. Derive an expression for the displacement of the rod, 0(t), in response to a step input of pressure of magnitude 100 Pa given the following data: 1, = 4 kgm²; c = 40 Ns/m; k= 500 N/m; L= 0.5 m; A= 0.2 m² Working from first principles, calculate the rise time, t,, of the system.

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
Problem 1.1MA
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Q4 Figure Q4 shows the schematic for a pressure pad. The pad has area A and is connected to a rod of length 6L which is free to rotate about its hinge point at 0. The rod is supported by a damper of coefficient c and a spring with stiffness k, in the positions shown. The rod has a moment of inertia I, about an axis through the pivot point, 0. The pad has a pressure P(t) applied to it which causes an angular displacement, 0, as indicated. (a) Assuming small angular displacements, derive an expression for the transfer function of the system relating angular displacement 0 to an input pressure P. Derive an expression for the displacement of the rod, 0(t), in response to a step input of pressure of magnitude 100 Pa given the following data: (b) 1, = 4 kgm2; c = 40 Ns/m; k = 500 N/m; L = 0.5 m; A = 0.2 m? (c) Working from first principles, calculate the rise time, t,, of the system. (d) Calculate the Maximum overshoot as a percentage value. P(t) 2L 2L 2L Figure Q4
Transcribed Image Text:Q4 Figure Q4 shows the schematic for a pressure pad. The pad has area A and is connected to a rod of length 6L which is free to rotate about its hinge point at 0. The rod is supported by a damper of coefficient c and a spring with stiffness k, in the positions shown. The rod has a moment of inertia I, about an axis through the pivot point, 0. The pad has a pressure P(t) applied to it which causes an angular displacement, 0, as indicated. (a) Assuming small angular displacements, derive an expression for the transfer function of the system relating angular displacement 0 to an input pressure P. Derive an expression for the displacement of the rod, 0(t), in response to a step input of pressure of magnitude 100 Pa given the following data: (b) 1, = 4 kgm2; c = 40 Ns/m; k = 500 N/m; L = 0.5 m; A = 0.2 m? (c) Working from first principles, calculate the rise time, t,, of the system. (d) Calculate the Maximum overshoot as a percentage value. P(t) 2L 2L 2L Figure Q4
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