1. ## Modelling Sinusoidal Equations

I figured that making a post asking how to do this would be a lot better than posting a bunch of different questions. I am having trouble setting up word problems that are given to me, such as

"A certain mass is supported by a spring so that it is at rest 0.5 m above a table top. The mass is pulled down 0.4 m and realeased at time t=0, creating a periodic up and down motion, called simple harmoic motion. It takes 1.2s for the mass to return to the low position each time. Draw a graphing shwing the height of the mass above the table top as a function for the first 2.0s. Write an equation for this function"

or

"A ferris wheel has a radius of 25 m, and its centre is 26 m above the ground. It rotates once every 50 s. Suppose you get on at the bottom at t=0. Draw a graph showing how your height above the ground changes during the first two minutes. Write an equation for this function"

I can graph the equation, Im just absolutely terrible at setting them up. Can anyone explain step by step? Thanks.

2. Originally Posted by xoKELLY
I figured that making a post asking how to do this would be a lot better than posting a bunch of different questions. I am having trouble setting up word problems that are given to me, such as

"A certain mass is supported by a spring so that it is at rest 0.5 m above a table top. The mass is pulled down 0.4 m and realeased at time t=0, creating a periodic up and down motion, called simple harmoic motion. It takes 1.2s for the mass to return to the low position each time. Draw a graphing shwing the height of the mass above the table top as a function for the first 2.0s. Write an equation for this function"

or

"A ferris wheel has a radius of 25 m, and its centre is 26 m above the ground. It rotates once every 50 s. Suppose you get on at the bottom at t=0. Draw a graph showing how your height above the ground changes during the first two minutes. Write an equation for this function"

I can graph the equation, Im just absolutely terrible at setting them up. Can anyone explain step by step? Thanks.
I can do the second one for you.

The general form of the sine function is:

$\displaystyle y = \alpha\sin{(\omega t + \phi)}$

The phase angle $\displaystyle \phi$ is $\displaystyle \frac{\pi}{2}$ since it starts at the maximum depth.

$\displaystyle \alpha$ is the amplitude, which in this case is 25m.

$\displaystyle \omega$ is the angular frequency, represented by:

$\displaystyle \omega = 2 \pi f$

$\displaystyle f$ is the frequency of the wave, represented by:

$\displaystyle f = \frac{1}{T}$

$\displaystyle T$ is the period, which in this case is 50s.

So, we have:

$\displaystyle \omega = \frac{\pi}{25}$

So, the equation is:

$\displaystyle y = 25\sin{\left(\frac{\pi}{25}t + \frac{\pi}{2}\right)}$

To verify:

$\displaystyle y = 25 \sin{\left(\frac{\pi}{25}(100) + \frac{\pi}{2}\right)}$

$\displaystyle y = 25 \sin{\left(4\pi + \frac{\pi}{2}\right)}$

$\displaystyle y = 25 \sin{\left(\frac{9\pi}{2}\right)}$

$\displaystyle y = 25m$

And there ya go.