# Thread: Find equation for trig word problem

1. ## 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.

2. 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.

3. 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?

4. 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?

5. 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!!

6. Originally Posted by pickslides
What is 3 quarters of 1.2?
I think its $0.9$

$\frac{3}{4}\times 1.2= \frac{3\times 1.2}{4} = \frac{3.6}{4}=0.9$

7. 36/40 = 9/10
9/10 = 0.9

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