Amass suspended on a spring will exhibit sinusoidal motion when it moves. if the mass on a spring is 85 cm off the ground at its highest position and 41 cm off the ground at its lowest position and takes 3.0 s to go from the top to the bottom and back again, determine an equation to model the data.

The equation of motion is

Explanation:

The general equation of motion of a SHM motion is given by

where,

A is the amplitude of the motion

ω is the natural frequency of the system

Since amplitude is defines as the maximum displacement of the object from the mean position we have

Now the time period is related to the natural angular frequency as

Thus the equation of motion becomes

the initial phase can be assumed to be zero thus the equation becomes

Using equation

y(t)=y0*Cos(wt)

w=2/3

y0=85-41

y(t)=44cos(2/3*t)

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