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 (0.75, 0) and the first maximum has coordinates (1.75, 2). (a) What is the period T of the periodic motion? T = 4 seconds (b) What is the frequency f in Hertz? What is the angular frequency w in radians / second? 25 Hertz %3D 1.57 radians / second (d) Determine the amplitude A and the phase angle y (in radians), and express the displacement in the form y(t) = Acos(wt - 7), with y in meters. y(t) = 0.04cos(pit-0.75pi) meters (e) With what initial displacement y(0) and initial velocity y' (0) was the system set into motion? y(0) 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 (0.75, 0) and the first maximum has coordinates (1.75, 2). (a) What is the period T of the periodic motion? T = 4 seconds (b) What is the frequency f in Hertz? What is the angular frequency w in radians / second? 25 Hertz %3D 1.57 radians / second (d) Determine the amplitude A and the phase angle y (in radians), and express the displacement in the form y(t) = Acos(wt - 7), with y in meters. y(t) = 0.04cos(pit-0.75pi) meters (e) With what initial displacement y(0) and initial velocity y' (0) was the system set into motion? y(0) 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 (0.75, 0) and the first maximum has
coordinates (1.75, 2).
(a) What is the period T of the periodic motion?
T = 4
seconds
(b) What is the frequency f in Hertz? What is the angular frequency w in radians /
second?
f =.25
Hertz
W =
1.57
radians / second
(d) 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) = 0.04cos(pit-0.75pl)
meters
(e) With what initial displacement y(0) and initial velocity y' (0) was the system
set into motion?
y(0) =
meters
y'(0) =
meters / second
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