(A) For a vibration system with transfer function below00θε=5s² + 2s+4(a) Calculate the damping ratio, damped natural frequency;(b) If the system is under unit step input, calculate the settling time and Maximum overshoot;(c) Obtain the complementary solution (transient response);(d) Obtain the particular solution (steady state response) when the system is under a step input:0₁ = 5(e) Determine the total system response if the system is initially at rest.(B) For the above system, please choose the correct answer for the following questions:(1) Which of the following curve is the Nyquist diagram of this control system:Imaginary Axis-0.5-10.51.51Nyquist Diagram-1.5-1-0.50.5Real AxisFigure 21.5C. Unstable(2) Is the system stable or not?A. StableB. Marginally stable(3) Which of the following Controller can eliminate the steady-state error of the system?A. P controller B. PI controllerC. PD controller D. ID controller

Given the transfer function θ(s) = 5 / (s² + 2s + 4), we can identify the coefficients of the…

Answered: (A) For a vibration system with…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A force of 5 pounds stretches a spring 1 foot. A mass weighing 6.4 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 1.2 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) = ft (b) Express the equation of motion in the form x(t) = Ae-At sin Vw2 – 2?t + p P), which is given in (23) of Section 3.8. (Round o to two decimal places.) x(t) = ft (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.)
A force of 4 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force numerically equal to 0.4 times the instantaneous velocity. (a) Find the equation of motion if the mass is initially released from rest from a point 1 foot above the equilibrium position. x(t) = ft (b) Express the equation of motion in the form x(t) = Ae-¹t sin(√w² - 2²t + p), which is given in (23) of Section 3.8. (Round up to two decimal places.) x(t) = ft (c) Find the first time at which the mass passes through the equilibrium position heading upward. (Round your answer to three decimal places.) S
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the relationship between aphids, A, ( prey) and ladybugs, L, (preditor) can be described as follows: dA/dt=2A=0.01AL dL/dt=-0.5L+0.0001AL a) find the two critical points of the predator-prey equations b) use the chain rule to write dL.dA in terms of L and A c) suppose that at time t=0, there are 1000 aphids and 200 ladybugs, use the Bluffton university slope field generator to graph the slope for the system and the solution curve. let 0 be less than or equal to A who is less than or equal to 15000 and 0 is less than or equal to L which is less than or equal to 400.
The spring constant of the system is K-2000 N/m and the damper is D=190 Ns/m. The mass is measured to be 600 Kg. The wheels are extremely well made and do not contribute in any significant way to the response of the cart system. fv ΔΧ(s) F(s) M X +'ve X Determine the transfer function describing the change in X from the resting location. This is denoted as Ax. ******* Make Note of positive direction of x and the direction of F *******
Consider a spring mass system with a 144 lb object attached. Suppose the object stretches the spring 18 inches in equilibrium. If the object is initially displaced 8 inches above equilibrium and given an initial velocity of -2 ft/s, find its displacement y in feet as a function of time t. Assume that this motion is undamped and that the spring is not deformed in the process. y(t) = feet
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انه e (A) For a vibration system with transfer function below 80 5 O s²+2s+4 (a) Calculate the damping ratio, damped natural frequency; (b) If the system is under unit step input, calculate the settling time and Maximum overshoot; (c) Obtain the complementary solution (transient response); (d) Obtain the particular solution (steady state response) when the system is under a step input: 0₁ = 5 (e) Determine the total system response if the system is initially at rest. (B) For the above system, please choose the correct answer for the following questions: (1) Which of the following curve is the Nyquist diagram of this control system: 1.5 Nyquist Diagram Imaginary Axis 0.5 -0.5 -1 (2) Is the system stable or not? A. Stable -0.5 0.5 1.5 Real Axis Figure 2 B. Marginally stable C. Unstable he nt e ns gu or
The dynamic model for a process is given by d2y/dt2+6dy/dt+8y=3u(t) where u(t) is the input function and y(0) and dy/dt(0) are both zero.What are the functions of the time (e.g.,e−t/τ) in the solutionfor each of the following cases?(a)u(t)=be−2t (b) u(t)=ct b and c are constants.Note:You do not have to find y(t) in these cases. Just determine the functions of time that will appear in y(t).
Suppose a 32-pound weight stretches a spring 2 feet. If the weight is released from rest at the equilibrium position, find the equation of motion x(t) if an impressed force f(t) = 20t acts on the system for 0 ≤ t < 5 and is then removed (see Example 5). Ignore any damping forces. Use a graphing utility to graph x(t) on the interval [0, 10].

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