# Find equation for trig word problem

• December 6th 2009, 12:10 PM
snypeshow
Find equation for trig word problem
the word problem is:

A mass is supported by a spring so that it is at rest 0.5 m above a tabletop. The mass is pulled down 0.4 m and released at time t = 0, creating a periodic up and down motion that can be modelled using a trigonometric function. It takes 1.2 seconds to return to the lowest position each time.

so i know it will be a sin(x) graph, and i know it starts 0.5m above ground level, therefore the vertical shift is 0.5m - that will give us:
y = a sin (x) + 0.5
the mass will be pulled down 0.4, and will rise 0.4 above where it was stationary (so 0.4m + 0.5m = 0.9m is the maximum). I can determine the amplitude: (0.9 - 0.8)/2 = 0.4, so that will give us:
y = 0.4 sin (x) + 0.5
the only two things i'm not sure about is the phase shift and the horizontal stretch.
• December 6th 2009, 12:46 PM
pickslides
Quote:

Originally Posted by snypeshow
It takes 1.2 seconds to return to the lowest position each time.

y = 0.4 sin (x) + 0.5
the only two things i'm not sure about is the phase shift and the horizontal stretch.

for the horizontal stretch consider

$y = 0.4 \sin (nx) + 0.5$ where $1.2 = \frac{2\pi}{n}$

for the phase shift think about the following. The sine wave needs to be shifted so it starts at a min.

alter the model to be

$y = 0.4 \sin (n(x-b)) + 0.5$ where b is the vertical shift.
• December 6th 2009, 12:53 PM
snypeshow
n = 5/3pi

but i don't understand how i would get b

EDIT: would the final equation be:

y = 0.4 sin (5/3pi [x-3/10]) + 0.5

because it's moved 3/10pi units?
• December 6th 2009, 01:04 PM
pickslides
The min value on the sine wave occurs exactly 3 quarters of the way through the length of 1.2 seconds. What is 3 quarters of 1.2?
• December 6th 2009, 01:09 PM
snypeshow
9/10? so the equation would be:

y = 0.4 sin (5/3pi [x-9/10]) + 0.5

i'm not sure if it's -9/10 or +9/10

but the standard form for the equation is y = a trig [ n ( x - h) ] + k

so since it's 9/10 (positive, not negative), and pos * neg = neg, i'm guessing it's:

y = 0.4 sin (5/3pi [x-9/10]) + 0.5

right?

EDIT: I just graphed it and found out it's +10 because it's moving right. thanks for your help!!
• December 6th 2009, 01:15 PM
pickslides
Quote:

Originally Posted by pickslides
What is 3 quarters of 1.2?

I think its $0.9$

$\frac{3}{4}\times 1.2= \frac{3\times 1.2}{4} = \frac{3.6}{4}=0.9$
• December 6th 2009, 01:18 PM
snypeshow
36/40 = 9/10
9/10 = 0.9
• December 6th 2009, 01:21 PM
pickslides
Quote:

Originally Posted by snypeshow
36/40 = 9/10
9/10 = 0.9

Totally mis-read what you wrote! (Doh)