Thread: 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.

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:



The phase angle is since it starts at the maximum depth.

is the amplitude, which in this case is 25m.

is the angular frequency, represented by:



is the frequency of the wave, represented by:



is the period, which in this case is 50s.

So, we have:



So, the equation is:



To verify:









And there ya go.