Question

A mass 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.

Answer 1

Answer:

Using equation

y(t)=y0*Cos(wt)

w=2$\pi$/3

y0=85-41

y(t)=44cos(2$\pi$/3*t)

Answer 2

Answer:

The equation of motion is $y(t)=22sin(\frac{2\pi }{3}t)$

Explanation:

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

$y(t)=Asin(\omega t+\phi )$

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

$2A=85 cm-41 cm\\\\A=\frac{44}{2}cm\\\\\therefore A=22cm$

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

$\omega =\frac{2\pi }{T}\\\\\therefore \omega=\frac{2\pi }{3}$

Thus the equation of motion becomes

$y(t)=22sin(\frac{2\pi }{3}t+\phi )$

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

$y(t)=22sin(\frac{2\pi }{3}t)$