1. A 150 g mass attached to a horizontal spring oscillates at a frequency of 3.4
ID: 1481556 • Letter: 1
Question
1. A 150 g mass attached to a horizontal spring oscillates at a frequency of 3.40 Hz . At t =0s, the mass is at x= 4.40 cm and has vx =? 29.0 cm/s . Determine the phase constant.
2. An air-track glider attached to a spring oscillates between the 16.0 cm mark and the 54.0 cm mark on the track. The glider completes 13.0 oscillations in 31.0 s . What is the maximum speed of the glider?
3. A 240 g particle moving along the x-axis experiences the force shown in the figure. (Figure 1) The particle goes from vx = 2.40 m/s at x =0m tovx = 6.00 m/s at x =2.0m.
What is Fmax?
Explanation / Answer
x = A*cos(wt-phi)
w = 2*pi*f = 2*pi*3.4 = 21.36 rad/s
at t = 0, x = 4.4 cm Vx = 29 cm/s
vx = w*(A^2-x^2)
29 = 21.36*(A^2-4.4^2)
A = 4.55 cm
spring constant k = m*w^2 = 0.15*21.36^2 = 68.44 N/m
at t = 0
4.4 = 4.55*cos((68.44*4.4)-phi)
phi = 301.4 rad
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2)
amplitude = (16+54)/2 = 35 cm = 0.35 m
time period = T = t/N = 31/13 = 2.4 s
Vmax = A*w = 0.35*2*pi/2.4 = 0.92 m/s
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3)
area = change in KE
0.5*F*2 = 0.5*0.24*(6^2-2.4^2)
F = 3.6288 N
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