1) For the mass-damper system at right, the model in terms of velocity ismv + cv = f. The time constant of this first order system is t = m/c.For this system, a larger value of the damping constant c causes the timeconstant to decrease - which is counterintuitive. It seems that a smallamount of damping should correspond to a system with a fast response.How can you reconcile this?mCA

Solution: Given Data: mv.+cv=fτ=mc To Find: Depend-ness of the time constant on the damping.

Answered: For the mass-damper system at right,…

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

See similar textbooks

Similar questions

1. Suppose you are riding your bicycle on a bumpy road having a surface profile that varies harmonically with +/- 6 cm undulations. The distance between consecutive peaks of these undulations is 2 m. When you sit on the seat of your bike for your casual ride, the springs deflect 5 cm. When you are seated, the damper under the seat provides an equivalent linear viscous damping of 10% of the critical damping. A simple representation of your ride on the "never-ending" rough road is shown below. (a) If you are riding your bicycle at a horizontal speed of 2.5 m/sec, how much bumping up and down will you experience? (b) Next day, you are carrying a backpack which increases your on-seat weight by 20%. Assuming that you are still able to ride with same speed, will this "loaded" ride be more or less comfortable than your previous, "no backpack" ride? M k/23 k/2 6 cm 2 m
What is the step response of the dynamic system pictured below?
(2) Please write out the Equation of Movements of the following system using matrix. (Figure 2) 1 Note: Lagrange's approach is recommended. „P₂(t) ks ww P₁(t) k₁ wwm, www k₂ m₂ k6 www P3(t) k₁ k3 www m3 www Figure 2: N Degree Vibration System
You are requested to design an automotive suspension or shock absorber system. In order to simplify the problem to one dimensional multiple mass-spring-damper system, a quarter vehicle model is used. The system parameters and free-body diagram of such system is shown below. M₁: Automobile body mass M₂: Wheel and suspension mass K₁: Spring constant of suspension system K2: Spring constant of wheel and tire B: Damping constant of shock absorber (a) Obtain the transfer function of X₁ (s) F(s) T₁(s) = = 2500 kg = 320 kg and T₂(s) = = 80,000 N/m = 500,000 N/m = 350 N-s/m Automobile- Suspension system Wheel- M₁ M₂ X₁ (s) - X₂ (S) F(s) in terms of the parameters of mass, damper and elastance (M, B and K). (b) Express the T₁ (s) and T₂ (s) with numerical values. c) Plot the x₁ (t) and x₁ (t) = x₂(t) outputs of this passive suspension system for the input torque f(t) = 2,000 N. fit) K₂ x₂(t) -Tire
Which one is the linearized modelling equation of the given system. 5-3Nm Your answer: O 22 + +72= fa(t) O2+6+11r fa(t) O 2+62 +9r= Ja(1)
Consider the following hydraulic / mechanical system, where pi and P2 are the inputs to the system, and the piston is driving a pendulum. Assuming small angles 0 and a concentrated mass ma distance L1 from the pivot. Pell (P2 R2 P1 Pa ¡P3 R1 P4 L2 Li Develop the dynamic equation to model of the piston displacement, 0, as a function of the inputs, p1 and p2 in standard form. b. If you were to consider the input to the system to be the difference between the pressure on 0(s) either side of the piston, write the transfer function for the displacement of the piston: AP(s) Xj = 0 c. Develop the state equations for this system if the state variables are:
Question 1: Determine the mathematical model of the linear mechanical system shown below, given f(t) is input force and x₁ (t), x₂ (t) and x3 (t) are output displacement for each mass. -x1(1) -X₂ (1) +x3(1) 1 N/m 1 N-s/m 1 N/m 1 N-s/m I oooo PAN 1 kg 1 kg0000 1 kg f(t)- HHHHH
Ex. A vehicle wheel, tire and suspension assembly can be modeled crudely as a single degree of freedom spring mass system. The mass of the assembly is measured to be about 300kg. its frequency of oscillation is observed to be π rad/sec. What is the approximate stiffness of the tire, wheel and suspension assembly? ilippines) Accessibility: Investigate
A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?
Derive a model for the mechanical system represented below. The input being the force F and the output the displacement x. Determine the time response, x(t) when F is an impulse force of 100 Newton. K-50 kg/s² M=10 kg B-60 kg/s F (Vol Ans: x(t) = 2.5(e¹ - es)
A mass-spring-dashpot system with constants k = 0,6, c = 0,7 and m = 100 g makes mechanical vibration. The system is exposed to no external force. If the system is at rest, initial position and velocity are 2 m and 6 m/sn, respectively. Under these circumstances, find the general equation of certain motion using the "Method of Laplace Transforms". 1. %3D

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Control Systems Engineering

Mechanical Engineering

ISBN:

9781118170519

Author:

Norman S. Nise

Publisher:

WILEY

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:

9781337093347

Author:

Barry J. Goodno, James M. Gere

Publisher:

Cengage Learning

Engineering Mechanics: Statics

Mechanical Engineering

ISBN:

9781118807330

Author:

James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher:

WILEY

SEE MORE TEXTBOOKS