Physic

The maximum speed of a mass attached to a spring is vmax = 0.438 m/s, while the maximum acceleration is 1.53 m/s2. What is the maximum displacement of the mass? (Answer: 0.125m)

Answer is provided above. Please show all work on how to get the answer. Thank you.

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  2. 👎 0
  3. 👁 53
  1. x = A sin w t
    v = A w cos wt
    a = -w^2 A sin wt = -w^2 x
    so
    A w = .438 or w = .438/A
    A w^2 = 1.53
    so
    A *(.438)^2/A^2 = 1.53
    so
    1.53 A = .192
    A = .125 m

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    posted by Damon
  2. max speed=max PE
    1/2 m v^2= 1/2 kx^2

    but me know max force=kx
    and force= ma so
    kx=1.53m

    1/2 mv^2=1/2 1.53m*x
    solve for x, m divides out.

    x=v^2/1.53 check that.

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