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
Answered question
2020-12-06
An object moves in simple harmonic motion with period 5 seconds and amplitude 7 cm. At time 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.
Answer & Explanation
crocolylec
Skilled2020-12-07Added 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 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:
Step 3
The amplitude is given by A, here since amplitude is 7 cm, so we have .
The period of the object is 5 seconds, so we have
Period
Step 4
Since the minimum displacement is at , so there is no phase shift,
so .
Also since there is no vertical shift, so
Thus the equation modeling the displacement d as a function of time t is given by:
The finalli equation modeling the displacement d as a function of time t is: