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

  1. Apr 5, 2004 #1
    Hello, it's me again. Yes Physics is most of my life right now. :tongue: 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 :biggrin: ).

    a(max)= Aω^2

    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!
  2. jcsd
  3. Apr 5, 2004 #2

    Doc Al

    User Avatar

    Staff: Mentor

    [tex]T = \frac{2 \pi}{\omega}[/tex]
  4. Apr 5, 2004 #3
    Of course! Lol. It's always the easiest things I overlook. Thank You!

    -The Village Idiot
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