(4 pts) The graph shows the displacement from equilibrium of a mass-spring syste
ID: 1494052 • Letter: #
Question
(4 pts) 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 minimum has coordinates (a) What is the period Tl of the periodic motion? T=12 seconds (b) What is the frequency fin Hertz? What is the angular frequency o) in radians/ second? f-0.5 Hertz radians / second (d) Determine the amplitude Al and the phase angle yn (n radians), and express the displacement in the form y(t) y(0) A cos(at- with Min meters. meters (e) With what initial displacement y(0) and initial velocity y '(0) was the system set into motion? meters y (0) meters / secondExplanation / Answer
The amplitude is 1.0 cm as the peak to peak dispalcement is 2.0 cm
The t intercept is 0.75,0
The pleading phase = 0.75 s converting it to radians
0.75/2 *2pi = 3pi/4 ( one period T = 2pi radians)
to express as Sin(wt+3pi/4)
or Cos(wt-3pi/4)
The dispalcment fucntion can be written as
y(t) = Cos(wt-3pi/4) cm
d) y(0) = Cos(3pi/4) = -0.71 cm
y'(0) = wSin(-3pi/4) = -2.22 cm/s
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