Period of a Mass on a Spring in Simple Harmonic Motion

In summary, the conversation discusses the calculation of the period of a bouncing truck at a construction site, taking into account its mass and the force constant of its springs. Part A involves calculating the period with a given mass and force constant, while part B discusses how the period would change if the truck was loaded with dirt. It is determined that a greater mass would result in a longer period, and the force constant could be considered as one big spring or distributed across all four wheels.
  • #1
pugfug90
118
0
Multiple force constants/Single mass?: SHM, Spring w/ mass.

Homework Statement


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?


Homework Equations


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


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)?
 
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  • #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?
 
  • #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.
 
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  • #4
hello..
PS, save mankind. Distribute your computing power:D
 
  • #5
PugFug, you don't need to plug numbers into 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.
 
  • #6
I know part b already.. Just wondering about part a..
 
  • #7
Just put the numbers you were given into the formula and calculate.
 
  • #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..
 

What is the Period of a Mass on a Spring in Simple Harmonic Motion?

The period of a mass on a spring in simple harmonic motion is the amount of time it takes for the mass to complete one full cycle of motion. It is measured in seconds and is influenced by the mass of the object, the spring constant, and the amplitude of the oscillation.

How is the Period of a Mass on a Spring Calculated?

The period of a mass on a spring can be calculated using the formula T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant. This formula is derived from the equation of motion for simple harmonic motion, x = A cos(ωt), where A is the amplitude and ω is the angular frequency.

What Factors Affect the Period of a Mass on a Spring?

The period of a mass on a spring is affected by three main factors: the mass of the object, the spring constant, and the amplitude of the oscillation. As the mass increases, the period also increases. Similarly, a higher spring constant or larger amplitude will result in a shorter period.

What is the Relationship Between Frequency and Period in Simple Harmonic Motion?

The frequency and period of a mass on a spring in simple harmonic motion are inversely related. This means that as the frequency increases, the period decreases, and vice versa. The formula for this relationship is f = 1/T, where f is the frequency and T is the period.

How is the Period of a Mass on a Spring Affected by Changing the Spring Constant?

The period of a mass on a spring is directly proportional to the square root of the spring constant. This means that as the spring constant increases, the period also increases. This relationship can be seen in the formula T = 2π√(m/k), where k is the spring constant.

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