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Period of a Mass on a Spring in Simple Harmonic Motion

  1. Mar 22, 2007 #1
    Multiple force constants/Single mass?: SHM, Spring w/ mass.

    1. The problem statement, all variables and given/known data
    Kim drives her empty dump truck over a berm (also called a speed bump) at the contruction site. The truck has a mass of 3000kg and the force constant for one of the truck's springs is 100,000N/m (Remember, truck has 4 wheels).

    a)What is the resulting period of the bouncing truck as it goes over the bump?
    b)If Kim leaves the contruction site with a load of dirt in her truck, what will this do to the period of her dump truck as truck crosses berm?

    2. Relevant equations
    http://people.scs.fsu.edu/~dduke/manual/Hooke_files/default_files/Hooke_files/Image294.gif [Broken]

    3. The attempt at a solution

    For part B, evaluating the equation and plugging in random numbers.. I'm pretty sure that more mass would result in a longer period..

    For part A, what's getting me is the (Remember, truck has 4 wheels) part.

    I can do T=2pi[square root (3000kg/(100000N/m)] which comes out to be 1.1s.. Or I don't know if I should multiply or divide or keep the 100000N/m by 4.. I think I've done as much work as I can without going in circles.. Would anyone like to tell me what I should do with the force constant (100000N/m)?
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Mar 22, 2007 #2
    a) I would just consider the four springs as one big spring with 4 times the spring force constant of one of them.
    b) What happens to the mass of the truck if it is loaded with dirt? How does T vary with m in the equation for the period?
  4. Mar 22, 2007 #3
    More dirt, more mass.. 50/2 is more than 12/2.. square root of 50/12 is more than 12/2 so yeah I'm pretty sure the period is going to be longer. PS, I'm plugging in random numbers for 50 and 12.
    Would like more responses.
    Last edited: Mar 22, 2007
  5. Mar 23, 2007 #4
    PS, save mankind. Distribute your computing power:D
  6. Mar 23, 2007 #5


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    Gold Member

    PugFug, you don't need to plug numbers in to see how mass affects the period. It's in the equation. If m gets bigger then so does T because they're both in the denominator. If k gets bigger T gets smaller because k is in the numerator - in other words you're dividing by k.
  7. Mar 23, 2007 #6
    I know part b already.. Just wondering about part a..
  8. Mar 24, 2007 #7


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    Gold Member

    Just put the numbers you were given into the formula and calculate.
  9. Mar 24, 2007 #8
    Did you take into consideration the 4 wheels, one wheel has force constant of 100,000N/m? That could mean a total of 400,000N/m or the stress being reduced across all 4 to 25,000 or the load being the same on all..
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