Answered: A vehicle circulates on a road as shown…

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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Transcribed Image Text:a) A vehicle circulates on a road as shown in Figure Q2a. The road profile can be modelled as the input u(t). The vehicle is modelled as a quarter car of mass m, and the suspension has a spring stiffness coefficient k = 2 Nm and a damper of coefficient c = 2 Nm s. Find the position of the mass, y(t) and any time t if the road profile is a unit step. m 一 Road Figure Q2a b) In Figure Q2b, a disk flywheel J of mass m 32 kg and radius r = 0.5 m is driven by an electric motor that when it is working produces an oscillating torque of Tin = 10sin(wt) N- m. The shaft bearings may be modelled as viscous rotary dampers with a damping coefficient of BR = 0.4 N-m-s/rad and stiffness coefficient KR = 2 Nm If the flywheel is at rest at t 0 and the power is suddenly applied to the motor, do the following [Hint:J = mr²/2]: (i) Find the natural frequency of oscillation of the disk expressed in Hz. (ii) Find the damping ratio for this system. (iii) Describe in no more than 3-4 lines the behaviour of the disk flywheel. bearing BR Flywheel J KR Tin(t) Figure Q2b

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