An object moves in simple harmonic motion with period 5 seconds and amplitude 7 cm. At time displaystyle{t}={0} seconds, its displacement d from rest is -7 cm, and initially it moves in a positive direction. Give the equation modeling the displacement d as a function of time t.

preprekomW 2020-12-06 Answered
An object moves in simple harmonic motion with period 5 seconds and amplitude 7 cm. At time t=0 seconds, its displacement d from rest is -7 cm, and initially it moves in a positive direction.
Give the equation modeling the displacement d as a function of time t.
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Expert Answer

crocolylec
Answered 2020-12-07 Author has 100 answers
Step 1
We need to find the equation that modeling the displacement d as a function of time t for an object moving in simple harmonic motion.
Step 2
At t=0 seconds, the displacement d is -7 cm, and moving in a positive direction. Since initially the object is at the lowest point and moving in positive direction, so we take the negative cosine function. So the general equation for displacement as a function of time t as:
d=Acos(BtC)+D
Step 3
The amplitude is given by A, here since amplitude is 7 cm, so we have A=7.
The period of the object is 5 seconds, so we have
Period =2πB
5=2πB
B=2π5
Step 4
Since the minimum displacement is at t=0, so there is no phase shift,
so C=0.
Also since there is no vertical shift, so D=0.
Thus the equation modeling the displacement d as a function of time t is given by:
d=Acos(BtC)+D
=7cos(2π5t0)+0
=7cos((2πt))5
The finalli equation modeling the displacement d as a function of time t is:
d=7cos(2πt5)
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Jeffrey Jordon
Answered 2021-10-26 Author has 2064 answers

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