Defining period (T) in terms of A(max) and V(max)

[new324]

Hello, it's me again. Yes Physics is most of my life right now. Here's one I'm not sure how to complete. Any hints/tips would be well appreciated. Thank You!

An object executing simple harmonic motion has a maximum speed v(max) and a maximum acceleration a(max). Find (a) the amplitude, A, and (b) the period, T, of this motion. Express your answers in terms of v(max) and a(max).

Well first I know I'm going to use the a(max) and v(max) formulas (duh ).

a(max)= Aω^2
v(max)=Aω

Well (a) is pretty cut and paste. Squaring v(max) yields A^2*ω^2
Put this over a(max), and the ω^2's cancel and the square of A cancels as well. So A= v(max)^2 / a(max)

Part (b) I'm having a little trouble finding the suitable equation to use. I thought about using, a= -ω^2*A*Cos(ωT). From here I saw a(max) cancels Aω^2 leaving -Cos(ωT)=1. However, only numbers (or radians) and a(max), v(max) can be used in the final solution. Any hints/tips? Much obliged!

 

[Doc Al]

T = \frac{2 \pi}{\omega}

 

[new324]

Of course! Lol. It's always the easiest things I overlook. Thank You!

-The Village Idiot