B. Write down a function y(t) that describes the position of the mass. Think car
ID: 1583663 • Letter: B
Question
B. Write down a function y(t) that describes the position of the mass. Think carefully about the phase shift!
C. What is the spring constant k? As always, include appropriate units.
D. If you doubled k, what would happen to the period T? If you doubled k and doubled m, what would happen to the period?
E. What is the unstretched length of the spring?
A mass m = 0, 1 kg is hanging from a spring ofunknown spring constant k. The mass's position y is measured from the attachment point of the spring, as shown. You observe the position vs time curve below. 05 2.5 t(s) A. What are the period T and amplitude A of the oscillation? What is the equilibrium length of the spring (with the hanging mass attached)?Explanation / Answer
A)
from the graph
A = 3 x 0.3 = 0.9 m
Time period is given as
T = 0.5 sec
B)
w = 2pi/T = 2 x 3.14/0.5 = 12.56 rad/s
at t = - 0.1 , y = 0.9
y(t) = A Cos(wt + phi)
0.9 = 0.9 Cos(12.56 (- 0.1) + phi)
1 = Cos(- 1.256 + phi)
phi = 1.256
so y(t) = 0.9 Cos(wt + 1.256)
C.
w = sqrt(k/m)
12.56 = sqrt(k/0.1)
k = 15.8 N/m
D)
Time period is given as
T = (2pi) sqrt(m/k)
when if we double the mass "m" and spring constant "k", the time constant T will remain same .
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