SHM - Equation for Displacement

[Peter G.]

Hi,

I just learned my first equation today in SHM:

x = x_o cos (ω * t)​

Firstly, is it ok if I change the "x =" part for a "y="? I get a bit confused since, from what I understand, we want to find the vertical distance from the x-axis and that would be the y output of a function. (x makes me think of the input)

I understand the first x, representing the displacement - stretching the graph parallel to the y axis.

Now, the (ω * t) part is what confuses me. Those values will determine where in the curve we want to find the displacement, correct? If so, how do the ω and time represent which part in the curve we are looking for, like the angles we input in our calculators do?

I hope I conveyed my doubts in a clear enough way,

Thanks,
Peter G.

My proble

 

[ideasrule]

Firstly, is it ok if I change the "x =" part for a "y="? I get a bit confused since, from what I understand, we want to find the vertical distance from the x-axis and that would be the y output of a function. (x makes me think of the input)

Sure. You can call your variables whatever you want, as long as you don't confuse yourself or the teacher.

Now, the (ω * t) part is what confuses me. Those values will determine where in the curve we want to find the displacement, correct? If so, how do the ω and time represent which part in the curve we are looking for, like the angles we input in our calculators do?

I don't understand what you mean by "where in the curve we want to find the displacement". The equation tells you the position of the oscillator for any given moment of time. So if I had an oscillator and I wanted to know where it's going to be at 10 seconds, I would calculate x0*cos(ω*10 s), and that would give me the answer.

 

[Peter G.]

Yes, what you mentioned is what I meant. Now, what role does ω have? Why do we have to multiply it by time to get the position in the cos curve, as we usually do by inputting angles in degrees or radians?