Simple Harmonic Motion: Question about w(t+T)=wt+2pi

[xtrubambinoxpr]

I have a quick question about simple harmonic motion. My text states this in the picture attached, and I'm confused as to why:

w(t+T) = wt+2pi
wT=2pi

I assumed w would distribute out into the first expression. I know this may be a dumb question but please help because it is bothering me.

Thank you!

 

[tiny-tim]

hi xtrubambinoxpr!

w(t+T) = wt+2pi
wT=2pi

I assumed w would distribute out into the first expression.

T is defined as being the time difference after which everything is the same.

So cos(ω(t+T)) = cos(ωt).

So ω(t+T) - ωt = 2π, ie ωT = 2π.

 

[xtrubambinoxpr]

hi xtrubambinoxpr!


T is defined as being the time difference after which everything is the same.

So cos(ω(t+T)) = cos(ωt).

So ω(t+T) - ωt = 2π, ie ωT = 2π.

i see my mistake! thanks!