Period of a Mass on a Spring in Simple Harmonic Motion

pugfug90

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



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)?

e(ho0n3

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?

pugfug90

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.
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Would like more responses.

pugfug90

hello..
PS, save mankind. Distribute your computing power:D

Mentz114

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.

pugfug90

I know part b already.. Just wondering about part a..

Mentz114

Just put the numbers you were given into the formula and calculate.

pugfug90

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..