Sinusoidal relationship

Question

Create a simple sinusoidal relationship, including 2 periods. With at least 9 columns (like let's say for a bicycle wheel). Like any numbers.

Answer 1

Hi Luhan,

For a bicycle wheel, let's measure the distance from the ground to one point on the wheel. Normally a sine function oscillates between -1 and 1, so we need a vertical shift to make the oscillation between 0 and the max height of the wheel. Let's assume the wheel is 2 feet diameter. So oscillation needs to be between 0 and 2.

f(x)=sin(x) (oscillation between -1 and 1)

Let's add 1 to the equation for a vertical shift of +1.

f(x)=sin(x)+1 (oscillation between 0 and 2)

where x is time in seconds and f(x) is the height of a point on the wheel. This point on the wheel starts in the middle between its min and max because its a sine function, unless we want to do a phase shift to start elsewhere.

So for two periods (nine columns):

f(x) = 1 2 1 0 1 2 1 0 1

x = 0 pi/2 pi 3pi/2 2pi 5pi/2 3pi 7pi/2 4pi

Hope this helps! :)