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Homework help: Harmonic Motion of a Spring and Block System

  1. Sep 15, 2011 #1
    1. The problem statement, all variables and given/known data

    Part 1:

    A 0.1 kg block attached to a spring of force constant 17.2 N/m oscillates with an amplitude of 16 cm. Find the the maximum speed of the block.

    I solved this part using the equations for angular frequency and max velocity.

    Part 2:

    Find speed of the block when it is 8 cm from the equilibrium position. Answer in m/s.

    Part 3:

    Find acceleration in the same situation ^

    Part 4:

    Find the time it takes the block to move from amplitude 0cm, to amplitude 8 cm.

    2. Relevant equations

    ω = [itex]\sqrt{}k/m[/itex]

    Vm = Aω

    V(t) = -AωSin(ωt)

    a(t) = - Aω^2Cos(ωt)


    3. The attempt at a solution

    Part 1 i figured out:

    ω = [itex]\sqrt{}17.2/0.1[/itex] = 13.1149 rads

    Vm = (.16)(13.1149) = 2.09838 m/s


    For part 2 i tried using the equation for velocity as a function of time. But i'm not sure how to solve the equation without the value for time. So far i have:

    V(t) = -(0.08)(13.1149)Sin(13.1149(t))


    Thank you everybody
     
  2. jcsd
  3. Sep 15, 2011 #2

    Hootenanny

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    Staff Emeritus
    Science Advisor
    Gold Member

    For part two, the displacement is half the amplitude so you are looking for a time [itex]t[/itex] such that [itex]\cos(\omega t) = 1/2[/itex].
     
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