I don't understand the derivation process here, help?

[Felix Gonzales]

Homework Statement

• I understand the derivation it showed that included the sin (15.7 in the image) I just don't understand the following (15.8 in the image). Does "t" get pulled out of the equation? If so what do we derive for then? Does it become 0? If so, it would remain 0 and sin(0) is just going to be 0, so that's not possible right? My issue is that I'm not sure how the sin and cos just disappear here.

Homework Equations

The Attempt at a Solution

• The only conclusion I drew was that somewhere between 15.7 and 15.8 and not before (allowing for the first few steps in 15.7) so I figured someone just erased all that out so they could be left with ωA. Though I doubt that's true and which is why I'd rather get a second opinion.

 

[Fightfish]

Equation (15.7) gives you the instantaneous velocity as a function of time, while Equation (15.8) gives you the expression for the maximum speed of the oscillation.

What is the maximum value of $\sin \omega t$?

 

[Felix Gonzales]

Equation (15.7) gives you the instantaneous velocity as a function of time, while Equation (15.8) gives you the expression for the maximum speed of the oscillation.

What is the maximum value of $\sin \omega t$?

*Edit* sorry I just saw the first half of your comment lol