The graph shows the displacement from equilibrium of a mass-spring system as a function of time after the vertically hanging system was set in motion at time t = 0. Assume that the units of time are seconds, and the units of displacement are centimeters. The first t-intercept is (0.25, 0) and the first minimum has coordinates (0.75, –3). (a) What is the period T of the periodic motion? T = 2 seconds (b) What is the frequency f in Hertz? What is the angular frequency w in radians / second? f = 1/2 Hertz W = 2pi/2 radians / second (c) Determine the amplitude A and the phase angle y (in radians), and express the displacement in the form y(t) = A cos(wt – y), with y in meters. y(t) .03cos(2pi/2(t+2.25)) meters (d) With what initial displacement y(0) and initial velocity y'(0) was the system set into motion? y(0) .03cos(2pi/2(2.2: H meters y'(0) meters / second
The graph shows the displacement from equilibrium of a mass-spring system as a function of time after the vertically hanging system was set in motion at time t = 0. Assume that the units of time are seconds, and the units of displacement are centimeters. The first t-intercept is (0.25, 0) and the first minimum has coordinates (0.75, –3). (a) What is the period T of the periodic motion? T = 2 seconds (b) What is the frequency f in Hertz? What is the angular frequency w in radians / second? f = 1/2 Hertz W = 2pi/2 radians / second (c) Determine the amplitude A and the phase angle y (in radians), and express the displacement in the form y(t) = A cos(wt – y), with y in meters. y(t) .03cos(2pi/2(t+2.25)) meters (d) With what initial displacement y(0) and initial velocity y'(0) was the system set into motion? y(0) .03cos(2pi/2(2.2: H meters y'(0) meters / second
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The graph shows the displacement from equilibrium of a mass-spring system as a function of time after the
vertically hanging system was set in motion at time t = 0. Assume that the units of time are seconds, and
the units of displacement are centimeters. The first t-intercept is (0.25, 0) and the first minimum has
coordinates (0.75, –3).
(a) What is the period T of the periodic motion?
T =
2
seconds
(b) What is the frequency f in Hertz? What is the angular frequency w in radians / second?
f =
1/2
Hertz
W =
2pi/2
radians / second
(c) Determine the amplitude A and the phase angle y (in radians), and express the displacement in the
form y(t) = A cos(wt – y), with y in meters.
y(t)
.03cos(2pi/2(t+2.25))
meters
(d) With what initial displacement y(0) and initial velocity y'(0) was the system set into motion?
y(0)
.03cos(2pi/2(2.2: H
meters
y'(0)
meters / second
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