How to calc the period of this mass spring system?

In summary, the conversation discusses finding the force that acts on a mass connected to two springs, as well as justifying the period of motion using forces or energy. It is suggested to measure the position of the connected springs without the mass, then attach the mass and measure the new position to find the effective spring constant. The solution also involves drawing free body diagrams and considering gravity when finding the period.
  • #1
LCSphysicist
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Homework Statement
How to calc the period of this mass spring system?
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This is a problem very easy to deal with if we consider the effective spring constant, however, i want to avoid this solution, and see how to justify the period of this motion just by analyse the forces or the energy, what seems a little hard to me.

First of all we would need to find the force that act on m, to do this we would need to find the stretched length of the spring touching the block, but to do this, we would need to know what is the displacement of the first spring too. ?

I don't know how to begin with it
 
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  • #2
First you should measure the position of the lowest end of the connected springs without the mass.
Then attach the mass, leave it at still and measure that position again.
mg / the difference of these positions = k of the connected springs. You will see it a half of k of one spring.
 
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  • #3
I was given this question by my teacher when I didn't know the effective spring constant.
My solution ended up deriving the effective spring constant by the end.
I think I assumed elongation in springs 1 and 2 to be ##x_1## and ##x_2## respectively, and then drew the free body diagrams for the joint of the springs and the block.
You might want to do this for springs with spring coefficients ##k_1 \text{ and } k_2## for more generality.

One more tip: When finding the period, you may want to assume that gravity doesn't exist to save some time.
The springs will have some initial elongation to account for the block's weight, so making this assumption would just result in the spring having no initial elongation. The period would remain the same.
 
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Related to How to calc the period of this mass spring system?

1. How do I determine the period of a mass spring system?

The period of a mass spring system can be calculated using the formula T = 2π√(m/k), where T is the period in seconds, m is the mass in kilograms, and k is the spring constant in N/m.

2. What is the significance of the period in a mass spring system?

The period represents the time it takes for the mass to complete one full oscillation or cycle in the spring system. It is an important factor in understanding the behavior and dynamics of the system.

3. Can the period of a mass spring system be changed?

Yes, the period of a mass spring system can be changed by altering the mass or the spring constant. Increasing the mass or decreasing the spring constant will result in a longer period, while decreasing the mass or increasing the spring constant will result in a shorter period.

4. What factors can affect the accuracy of calculating the period of a mass spring system?

The accuracy of calculating the period can be affected by factors such as air resistance, friction, and the elasticity of the spring. These factors can introduce external forces that can alter the motion of the mass and affect the period.

5. Are there any real-life applications of calculating the period of a mass spring system?

Yes, the concept of a mass spring system and its period is used in various fields such as engineering, physics, and mechanics. It is commonly used in designing and analyzing structures such as bridges, buildings, and mechanical systems.

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