Amass suspended on a spring will exhibit sinusoidal motion when it moves. if the mass on a spring is 91 cm off the ground at its highest position and 27 cm off the ground at its lowest position and takes 3.6 s to go from the top to the bottom and back again, determine an equation to model the data.

Assume that the mass start at a height of (its equilibrium position.)

,

where

Step-by-step explanation:

A mass on an ideal, vertical spring is in a simple harmonic motion. Its displacement from its equilibrium position at time can be modelled with a sine equation:

,

where

For convenience, assume that , such that the object starts at equilibrium position.

.

.

The equation would become:

,

The height of the object at equilibrium position is the average between its max and min height. . To find the height of the object, add its height at equilibrium to the displacement from its equilibrium position.

Hence the equation:

.

1. 8

2. 9

3. 20

4. 3

5. 17

6. 2.2

7. 11.25

8. 1

9. 14

10. 2

step-by-step explanation:

thats the first half