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Spring block system

  1. Apr 2, 2005 #1
    a 1 kg mass attached to a spring with a force constant of 25 oscillates on a horizontal, frictionless track. At time t=0, the mass is released from rest at x=-3cm (the spring is compressed by 3cm). Find (a) the period of its motion. b) the max values of speed and acceleration. c) the displacement, velocity, acceleration as a function of time.

    a)
    [tex]T=2\pi \sqrt{\frac{m}{k}}[/tex]
    [tex]T=2\pi \sqrt{\frac{1kg}{25N/m}}[/tex]
    [tex]T=1.257s[/tex]

    b)
    [tex]v_{max}=\omega A=\sqrt{\frac{k}{m}}*A =\sqrt{\frac{25}{1}}*0.03=0.15m/s[/tex]
    [tex]a_{max}=\omega ^2 A=\frac{kA}{m} ={\frac{25}{1}}*0.03=0.75m/s^2[/tex]

    c)
    [tex]x=-0.03cos25t[/tex]
    [tex]v=0.15sin25t[/tex]
    [tex]a=0.75cos25t[/tex]

    is this all correct?
     
    Last edited: Apr 2, 2005
  2. jcsd
  3. Apr 2, 2005 #2

    quasar987

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    Looking sexy.
     
  4. Apr 2, 2005 #3
    so the period does not involve how much was pulled back?
     
  5. Apr 2, 2005 #4

    quasar987

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    Nah.

    And this is understandable since if you pull the block back a lot, sure it has a "longer way to go" to the equilibrium position, but it has more energy at its disposal.
     
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