5- A system and its response are given in following Figures,the values of M, B and K.determinereeeeeBy(t)=8.9x(t)0.030.0029

Given: The peak overshoot time is tp=2 sec. The function is yt=8.9. Concept used; The equation of…

Answered: 5- A system and its response are given…

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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1) Guess the form and solve for the particular solution of a driven oscillator described by the equation: mx" + cx' + kx = Fosin(wt) 2) A mass of 4 kg on a spring with k = 4 N/m and a damping constant c = 1Ns/m is driven by a force following the function Focos(at); where FO = 2 N. Find the driving frequency that causes practical resonance and find the amplitude. 3) Suppose there is no damping in a mass and spring system with m = 5, k = 20, and Fo= 5. Suppose is chosen to be precisely the resonance frequency. a) Find a b) Find the amplitude of the oscillations at time = 100, given that the system is at rest at / = 0.
Response using matlab.
You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 d) Knowing that the distance travelled by an object is the area under its velocity-time graph, determine the distance travelled by the end effector on the interval 0 =< t =< 1 by using the mid-ordinate rule. Simpson’s rule correct to 3 decimal places using four intervals. e) Calculate the same distance as in (d) above by using the appropriate definite integral. f) Compare the distances you calculated in (d) and (e) above and comment on the accuracy of the two methods you used in (d)
You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 Use your knowledge of differentiation to sketch the velocity-time graph, clearly marking the critical points. Using the graph sketched in (a) above, estimate the velocity when t = 1.5 s Calculate the velocity of the function when t = 1.5 s by substituting to the velocity function. Compare this value to the value you estimated in b above.
6. The figure below represents a time response of a control system. y(r) 0.63 What is it? a) Unit-step response of a Prototype First-Order System; b) Unit-Impulse Response of a Prototype First-Order System; c) Unit-Step Response of a Prototype Second-Order System; d) Unit-Impulse Response of a Prototype Second-Order System.
A mechanical system is represented by two masses and three springs, where m, = 12 kg, m, = 22kg, and spring constants k, = k, = k, = 15 N/m, as shown in the following figure. k3 m2 Determine the largest eigenvalue of this mechanical system using the characteristic equation. a. b. Determine the smallest eigenvalue and the corresponding eigenvector using Inverse Power method. Given the initial eigenvector v(0)= (1 1 1). Iterate until | Ar41 - 1x 50.0005.
Draw by hand the Bode plot of the following systems. 1. 50 G(s) : s(s² + 4s + 8) 2. 20(s + 1) s(s² + 2s + 10)(s + 5) G(s) =
Solve the initial value problem. y" + 4y' + 20y = 0: y(0) = 2 y (0) = - 3 %3D Chapter 6, Section 6.2, Go Tutorial Problem 12 Find Y(s). 2s + 5 Y(s): s2 + 4s + 20 2s + 5 Y(s) = s2 + 4s + 20 2s – 5 Y(s) : + 4s + 20 2 + 4s + 20 Y(s) 2s + 5
:) Determine the equivalent mass of the system shown in Figure Q.A3c. X m 2r m Figure Q.A3c. m WE For the system shown in Figure QA1a write appropriate response variables and find the degrees of freedom. r= 10 cm /= 1.5 kg-m² m = 10 kg nollos 2k
A mechanical system is represented by two masses and three springs, where m, =12 kg, m, = 22kg, and spring constants k, = k, = kg = 15 N/m, as shown in the following figure. m2 Determine the largest eigenvalue of this mechanical system using the characteristic equation. а. Determine the smallest eigenvalue and the corresponding eigenvector using Inverse Power method. Given the initial eigenvector v(0)=(1 1 1)". Iterate until |ak+1 - 2x IS0.0005. b.
5 Problem Match the following two frequency response diagrams: -0 0.4 |G(i w)| 0.2 10 |G(i w)| 5 Response A 2 3 4 5 6 7 8 Frequency, (rad/s) Response B 5 6 7 8 Frequency, w(rad/s) 1 2 3 4 6 6 10 10 10 to two of the following ODES 1. +x+100x = u(t) 5. +100x = u(t) 9. +100x = u(t) 3. x+x+5x= u(t) 4. x+x+x= u(t) 2. x+x+25x = u(t) : 6. x + 25xu(t) 10. +25x = u(t) 7. x+5x= u(t) 8. u(t) 11. +5x= u(t) = 12. xu(t)
2- Using Matlab, what are the step response curves of the closed-loop system, as shown in fig.1. the feedback represents the second-order dynamic system. (fill in the following table) For=0.4 Wn 1 3 6 9 10 R(S) 0.1 0.3 0.6 0.9 1 For w 5 rad/sec 3 Settling time Peak response 2 Wn s(s+23wn) Settling time Peak response C(s) Discuss the follow Which parameters or w occur on the rise time of the response? Which parameter increases the speed of response? Which parameters can be decreases the response amplitude? Which parameter decreases the steady error state? fig.2

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5- A system and its response are given in following Figures, determine the values of M, B and K. y(t)=8.9 x(1) 0.03 0.0029