Fig. (2)Q3-A (8 Marks): An automobile is modeled as a single-degree-of-freedom system vibrating inthe vertical direction. It is driven along a road whose elevation varies sinusoidally. Thedistance from peak to trough is 0.2 m and the distance along the road between the peaks is 35m. If the natural frequency of the automobile is 2 Hz and the damping ratio of the shockabsorbers is 0.15, determine the amplitude of vibration of the automobile at a speed of 60km/hour6.18

First, we need to convert the speed of the automobile from kilometers per hour to meters per second.…

Answered: Fig. (2) Q3-A (8 Marks): An automobile…

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) For the mass-damper system at right, the model in terms of velocity is mv + 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 time constant to decrease - which is counterintuitive. It seems that a small amount of damping should correspond to a system with a fast response. How can you reconcile this? m CA
Whats the first equation (circled) and how did we get it ?
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
2.10 Derive the equation for the displacement response of a viscously damped SDF system due to ini- tial velocity u(0) for three cases: (a) underdamped systems; (b) critically damped systems; and (c) overdamped systems. Plot u(t) : u(0)/w, against t/T, for 5 =0.1, 1, and 2.
A toddler with a mass of 14.4 kg bounces up and down in her crib. The crib mattress behaves like a light spring with force constant 1840 N/m. (a) The toddler bounces with at a frequency that allows her to reach a maximum amplitude with minimum effort. What is this frequency (in Hz)? Hz (b) The toddler now bounces high enough to lose contact with the mattress once each cycle, like a trampoline. What is the minimum amplitude of ocillation (in cm) required for this to occur? cm Need Help? Read It
Example 2.9 Determine the maximum responses of a water tower which is subjected to a sinusoidal force of amplitude 445 kN and frequency 30 rad/s over 0.3 secs. The tower has properties, mass 17.5 t, stiffness 17.5 MN/m and no damping. Ans. 120 mm, 3.8 m/s, 120.7 m/s²
A boxcar moving at 1.7 m/s hits the shock absorber at the end of the track. The boxcar mass is 20,000 kg. The stiffness of the absorber is k = 100,000 N/m, and the damping coefficient is c = 40,000 N-s/m. The box car and shock absorber act as one system for a brief period while in contact. a. Make dynamic model (define system equation) for the boxcar and shock absorber system. Then, numerically simulate the system response starting at the point of contact and ending after 6 seconds. Plot the spring force, boxcar velocity, and boxcar displacement as functions of time. b. State the maximum spring deflection. Note that once the boxcar loses contact, the model is no longer valid. Model is not valid for the entire 6 seconds. At what point in time is contact lost? c. What is the boxcar velocity when contact is lost? H m ====== k
Q2 The angular position c of a mass is controlled by a servo system through a referen signal °r. The moment of inertia of moving parts referred to the load shaft, J, is 150 kebo and damping torque coefficient referred to the load shafi(B, is 4.5 x 103 Nw-m fraden The torque developed by the motor at the load s 7.2 x 10* Nw-m per radian of error (a)Obtain the response of the system to a step input of 1 rad and determine the peak time, peak overshoot and frequency of transient oscillations. Also find the steady state error for à constant angular velocity of 1 revolution / minute. (b)If a steady torque of 1000 Nwm is applied at the load shaft, determine the steady Kan state error. 5(J5+ B) 03 For the system shown, apply a proportional controller to move the time constant to a sixth of its open loop value. R(s) + E(s) U(s) Kp 'Y(s) s +0.333 10
A baby with a mass of 10.6 kg bounces up and down in his crib. The crib mattress behaves like a light spring with force constant 506 N/m. (a) The baby bounces with at a frequency that allows his to reach a maximum amplitude with minimum effort. What is this frequency (in Hz)? Hz (b) The baby now bounces high enough to lose contact with the mattress once each cycle, like a trampoline. What is the minimum amplitude of oscillation (in cm) required for this to occur? cm
An object attached to the end of a vertical helical spring bounces with a frequency of 2.1 Hz. If the spring constant is 5.9 N/m, what is the mass of the object?
3
MECHANICAL VIBRATIONS An unknown mass m is attached to the end of a linear spring with unknown stiffness coefficient k. The system has natural frequency of 30 rad/s. When a 0.5 kg mass is added to the unknown mass m, the natural frequency is lowered to 20 rad/s. Determine the mass m and the stiffness coefficient k.

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