3 spring shock absorber help

In summary, the problem involves determining the frequency of vibrations and the maximum vertical deflection of an egg attached to a structure using rubber bands. The effective spring constant is found by considering the three springs in parallel, and the frequency can be calculated using this constant and the mass of the egg. The maximum vertical deflection can be found using the equation for simple harmonic motion and the initial conditions of the system.
  • #1
Whitebread
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0

Homework Statement


The problem verbatim from the text:
"One of the winners in an egg-drop contest was a structure in which rubber bands held the egg at the center of it. Attached is a model. Consider the egg to be a particle of mass m and the springs to be linear with spring constants k. consider only a two dimensional version of the winning design as shown in the figure attached. Assume the frame hits the ground on one of the straight sections. Assume small motions (deflection << side-length) and that the springs do not buckle.
a)What will be the frequency of the vibrations after the impact?
b) what is the maximum vertical deflection of the egg (relative to its equilibrium position)?


Homework Equations


f=1/t=2*(pi)*sqrt(k/m)
x(t)=Asin(wt+phi) A=amplitude

The Attempt at a Solution


I've been dwelling on this question for a while and I've been unable to completely solve it (obviously). Using law of cosines, the initial and final lengths of the side springs and deltaX (the change in length of the top spring), I have derived that the length of the side springs after deflection is approximately equal to:
L'=sqrt(lo^2-lo*x)
This is assuming that deltaX is extremely small and when squared in the law of cosines, goes to 0.

In order to find the frequency, I need to find the effective spring constant, because:
f=1/T=2*(pi)*sqrt(k/m)
but I don't quite know where to go from here. Did I make an incorrect approach?
I have not made an attempt at part b
 

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  • #2
) yet.




Thank you for sharing your approach to this problem. It seems like you have made some progress in your calculations, but there are a few areas that could use some clarification and further explanation. Let me address them one by one:

1. Effective spring constant: In order to calculate the frequency of the vibrations, you need to find the effective spring constant of the system. This can be done by considering the equivalent spring constant of the three springs in parallel. This means that the effective spring constant will be equal to the sum of the individual spring constants. In this case, the top spring is stretched by a distance x, while the side springs are compressed by the same amount. Therefore, the effective spring constant can be written as:

k_eff = k + k + k = 3k

2. Frequency calculation: With the effective spring constant, you can now calculate the frequency of the vibrations using the formula you mentioned:

f = 1/T = 2*pi*sqrt(k_eff/m)

Note that the mass, m, in this case, will be the mass of the egg. Also, keep in mind that the period, T, is equal to the time it takes for one complete vibration, which is the same as the time it takes for the egg to return to its original position after being dropped.

3. Maximum vertical deflection: To calculate the maximum vertical deflection of the egg, you can use the equation for simple harmonic motion that you mentioned:

x(t) = A*sin(wt + phi)

In this case, the amplitude, A, will be equal to the maximum vertical deflection, and the angular frequency, w, can be calculated using the formula:

w = 2*pi*f

You will also need to determine the phase angle, phi, which can be found using the initial conditions of the system (i.e. the initial displacement and velocity of the egg when it hits the ground).

I hope this helps guide you towards a solution to this problem. Good luck!
 

What is a 3 spring shock absorber?

A 3 spring shock absorber is a type of suspension system used in vehicles to absorb shock from the road and provide a smoother ride. It consists of three springs that work together to absorb and dissipate energy when a vehicle encounters bumps or uneven surfaces.

How does a 3 spring shock absorber work?

The three springs in a 3 spring shock absorber work together to minimize the impact of bumps and vibrations on a vehicle. The primary spring supports the weight of the vehicle, while the secondary and tertiary springs help to absorb and dissipate energy as the vehicle moves over uneven surfaces.

What are the benefits of using a 3 spring shock absorber?

Using a 3 spring shock absorber can provide a smoother and more comfortable ride for passengers by reducing the impact of bumps and vibrations on the vehicle. It can also improve the handling and stability of the vehicle, especially on rough terrain.

How do I know if my 3 spring shock absorbers need to be replaced?

Some signs that your 3 spring shock absorbers may need to be replaced include a bouncy or uncomfortable ride, uneven tire wear, and excessive noise or vibrations while driving. It is recommended to have your shock absorbers inspected by a mechanic regularly to ensure they are functioning properly.

Can a 3 spring shock absorber be installed on any vehicle?

No, a 3 spring shock absorber is designed for specific types of vehicles and may not be compatible with all makes and models. It is important to consult with a professional mechanic or refer to the manufacturer's specifications to determine if a 3 spring shock absorber is suitable for your vehicle.

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