The graph shows the displacement from equilibrium of a mass-spring system as a f

Question

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 f-intercept is (0.75,0) and the first minimum has coordinates (1.75,-4). What is the period T of the periodic motion? T = seconds What is the frequency/in Hertz? What is the angular frequency w; in radians/second? F = Hertz W= radians/second Determine the amplitude A and the phase angle gama (in radians), and express the displacement in the form y(t) = A cos(wt - gama), with y in meters. y(t) = meters With what initial displacement y(0) and initial velocity y '(0) was the system set into motion? Y'(0) = meters y'(0) = meters/second

Explanation / Answer

a)
1 wavelength of graph is spread across 4s
So,
T = 4 s

b)
f = 1/T
= 1/4
= 0.25 hZ

w = 2*pi*f
= 2*pi*0.25
=1.57 rad/s
  
d)
Amplitude, A = 4 m

phase = -0.2 s
= -0.2*2*pi/T rad
= -0.2*2*pi/4 rad
   = -0.314 rad
  
y(t) = A*cos (wt-phase)
= 4* cos (1.57*t +0.314)
     
e)
y(t) = 4* cos (1.57*t +0.314)
y(0) = 4* cos (1.57*0 +0.314)
= 4* cos (0.314)
   = 3.8 m

y(t) = 4* cos (1.57*t +0.314)
y'(t) = - 4*1.57* sin (1.57*t +0.314)  
y'(0) = - 4*1.57* sin (0.314)     
= -1.94 m/s

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.