Question 1035649: An object's motion is described by the equation: d=5cos(pi/3(t))
The displacement d, is measured in meters. The time t, is measured in seconds.
Answer the following questions, showing all work:
(a) What is the object's position at t=0?
(b) What is the object's maximum displacement from its equilibrium position?
(c) How much time is required for one oscillation?
(d) At what time will the object first reach its equilibrium position (hint: d=0)?
Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! An object's motion is described by the equation: d=5cos(pi/3(t))
The displacement d, is measured in meters. The time t, is measured in seconds.
Answer the following questions, showing all work:
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t is in the numerator.
d=5cos(pi*t/3)
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(a) What is the object's position at t=0?
Sub zero for t.
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(b) What is the object's maximum displacement from its equilibrium position?
The amplitude, 5 meters.
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(c) How much time is required for one oscillation?
6 seconds.
P = 2pi/(pi/3) = 6
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(d) At what time will the object first reach its equilibrium position (hint: d=0)?
d=5cos(pi*t/3) = 0
cos(pi*t/3) = 0 = cos(pi/2)
pi*t/3 = pi/2
t/3 = 1/2
t = 1.5 seconds
Answer by Boreal(15235)  (Show Source):
You can put this solution on YOUR website! At t=0, the function is d=5 cos (0)=5
The maximum displacement is the cosine coefficient or 5.
For one oscillation, the period, it is 2pi/(pi/3)=6
For the equilibrium position, it is one-quarter of the period, or 1.5 pi/3
and 4.5 pi/3. The cosine is 1 at 0, 0 at pi/2 and again at 3pi/2
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