An Oscillatory system consists of a mass, m = 120 slugs, a spring constant, k = 40 lb/in, and a damping coefficient, c = 5lb.sec/in. Determine a.The natural frequency. b.The damping ratio. c.The damped frequency. d.The maximum amplitude if u0 = 0.2in and v0 = 0.5in/sec.

An Oscillatory system consists of a mass, m = 120 slugs, a spring constant, k = 40 lb/in, and a damping coefficient, c = 5lb.sec/in. Determine a.The natural frequency. b.The damping ratio. c.The damped frequency. d.The maximum amplitude if u0 = 0.2in and v0 = 0.5in/sec.

Automotive Technology: A Systems Approach (MindTap Course List)

6th Edition

ISBN:9781133612315

Author:Jack Erjavec, Rob Thompson

Publisher:Jack Erjavec, Rob Thompson

Chapter22: Basics Of Electronics And Computer Systems

Section: Chapter Questions

Problem 7RQ

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Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

I need help with part D, I 've attached A/B/C, please help

An Oscillatory system consists of a mass, m = 120 slugs, a spring constant, k = 40 lb/in, and a damping coefficient, c = 5lb.sec/in. Determine

a.The natural frequency.

b.The damping ratio.

c.The damped frequency.

d.The maximum amplitude if u0 = 0.2in and v0 = 0.5in/sec.

a) Natural angular frequency
40
W. =
3860.89
W. = 0. 1018 radlsec
natural frequency, fa =
2x
f.
0.1018
f, = 0.0162 Hz
Step 3
b) Damping ratio =
2mw.
E =
2x 3860.89 10.1018
E = 0.00636
c) Damped frequency
Wa = V1 - e wn
VI - (0.00636)? x0. 1018
Wa = 0. 101798 rad/sec
Wa

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