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Periodic Motion

  1. May 7, 2007 #1
    1. The problem statement, all variables and given/known data
    A 500g block is attached to a spring on a frictionless horizontal surface. The block is pulled to stretch the spring by 10cm, then gently released. A short time later, as the block passes through the equilibrium position, its velocity is 1m/s.
    >A)What is the block's period of oscillation?
    >B)What is the block's speed at the point where the spring is compressed by 5cm?

    2. Relevant equations
    T = 2(pi)sqrt(I/mgd)

    3. The attempt at a solution
    I'm having troubles starting this problem. I'm thinking since it's 1m/s at it's equilibrium position (5cm) then it take 20seconds for half a cycle? That sounds completely wrong. I need some help.
     
    Last edited: May 7, 2007
  2. jcsd
  3. May 7, 2007 #2
    Have you encountered an equation that looks like x=Asin(w*t) ??

    This is a general eqn for describing simple harmonic motion, which is what this problem is about. It also describes the motion of a pendulum.

    w*t (angular velocity * time) in the sine expression above, is the key to answering this problem as it also determines the period thru the relation,

    T=2*pi/w.

    So how to determine w?

    Well if we were given a value of time and position we could do so as we are given A, the amplitude, as equal to 10cm.

    But all we are told is that a "short time later", its velocity is 1m/s as it passes thru the equalibrium point. That is when x=0.

    We can differentiate the above expression with respect to time to get,

    dx/dt=v=w*A*cos(wt). Since we know that x=0, it follows sin(wt)=0 at that time, and most importantly for the purposes of this problem cos(wt)=1 at the same time, so we can substitute 1 for cos(wt).

    Can you finish from here?
     
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