Vector Mechanics For Engineers
12th Edition
ISBN: 9781259977305
Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.
Publisher: Mcgraw-hill Education,
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Chapter 19.5, Problem 19.129P
To determine
Show that the logarithmic ratio of two successive maximum displacement is equal to
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Problem 2.121: Variation of Displacement
Find the variation of the displacement with time, x(t), of a damped single-
degree-of-freedom system with m=10 kg, k=10,000 N/m, and 3-=0.1 for the
following initial conditions:
(a) x(0)=0.2 m, x(0)=0, (b) x(0)=-0.2 m, x(0)=0
(c) x(0)=0, x(0)=0.2
m
sec
A single degree of freedom mass-spring-damper system is subject to vibration under the influence of a harmonic force. On my site, it is given as m=2 kg, k=800 N/m, c=64 Ns/m. The amplitude of the harmonic force is F0=256 N and its frequency is w= 20 rad/s. Answer the questions in options a, b, and c according to the given information.
1) Calculate the damping ratio of the system (ξ)
a.1 b.0.7 c.0.9 d.0.8
2)Calculate the magnification factor (M) of the system.
a.0.86 b.1.25 c.0.312 D.0.625
3-) Calculate the maximum vibration amplitude (X) (meters).
a.0.2 b.0.1 c.0.4 D.0.3
An undamped simple harmonic oscillator has mass 2.0 kg and spring constant 50
N/m. The initial displacement from equilibrium (at time t = 0) is 0.30 m and the
initial velocity is 2.0 m/s.
%3D
1. Determine the angular frequency (in rad/s), the frequency (in Hz), and the
period (in s). Determine numerical values (not in terms of .) Determine the
displacement in the form x(t) = Acos(mot) + Bsin(@ot). That is, solve for A and B in
meters, and write oo in radians per second.
Chapter 19 Solutions
Vector Mechanics For Engineers
Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3PCh. 19.1 - Prob. 19.4PCh. 19.1 - Prob. 19.5PCh. 19.1 - A 20-lb block is initially held so that the...Ch. 19.1 - Prob. 19.7PCh. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9PCh. 19.1 - A 5-kg fragile glass vase is surrounded by packing...
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