An object moves in simple harmonic motion with period 7 seconds and amplitude 3cm. At time =t0 seconds, its displacement d from rest is 0cm, and initially it moves in a negative direction. Give the equation modeling the displacement d as a function of time t.

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aristeus aristeus · Answer 1 · 2019-12-03T09:33:00+01:00

Answer:

The equation will be [tex]d(t)=-3sin(\frac{2\pi }{7}t+\frac{-2\pi t_0}{7} )[/tex] ( as it moves first in negative direction )

Step-by-step explanation:

We have given that object is moving in SHM

So the equation of motion is either cosine or sine in nature

We can assume formula

[tex]d(t) = Asin(ωt + Ф)[/tex]

We have given

Amplitude A =3

Time period = 7 sec

We know that [tex]\omega =\frac{2\pi }{T}=\frac{2\pi }{7}[/tex]

So [tex]d(t)=3sin(\frac{2\pi }{7}t+\frac{-2\pi t_0}{7} )[/tex]

At t = [tex]t_0[/tex] sec displacement is 0

So [tex]0=3sin(\frac{2\pi }{7}\times [tex]t_0[/tex]+\Phi )[/tex]

[tex]\Phi =\frac{-2\pi t_0}{7}[/tex]

So the equation will be [tex]d(t)=-3sin(\frac{2\pi }{7}t+\frac{-2\pi t_0}{7} )[/tex] ( as it moves first in negative direction )