Section 6.3: Exploring Classical Probability Distributions

xi = | xf = | PR(x) =

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The relative probability distribution, PR(x), is shown. For bound systems, where a particle will always be in a certain finite region of space, this distribution can be normalized to yield a normalized probability distribution, PN(x).  Restart.

  1. Calculate the relative probability distribution, PR(x),  for a 1-kg particle initially at rest and attached to a spring (a harmonic oscillator) of spring constant k = 2 N/m and an initial displacement from equilibrium of 1 m.
  2. Now enter in this function into the text box and set the proper classical limits by clicking the "change limits and evaluate" button. What is the normalized classical probability distribution,  PN(x)?  You must normalize (a) by doing the integral.

Repeat (a) and (b) for a 0.1-kg particle dropped from rest 1 m above the ground. Assume an elastic collision with the ground at y = 0 m.

Once you have completed your calculations, check your results using the animations provided below.

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