How do I calculate the period for a system with 2 springs and 1 mass in series?

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In summary, the conversation discusses a physics problem involving springs in series and Hooke's law. The goal is to find the effective spring constant and the period of oscillation. The conversation includes attempts at solving the problem and helpful resources for finding the solution.
  • #1
Matt1234
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Homework Statement


[PLAIN]http://img24.imageshack.us/img24/2706/64505257.jpg


Homework Equations



t = 2pi * Sqrt(m/k)

The Attempt at a Solution



Im not very sure how to proceed with this one. I have tried calculating the peroid for 2 separate cases and then adding them together but it didnt seem to give the same result as the question. I am not looking for the answer, instead some direction on how to obtain it. I have also tried starting from hookes law.
 
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  • #2
Use Hooke's law to figure out the effective spring constant in each case.
 
  • #3
EDIT: Note there should be a + in between kx1 and kx2, sorry.

Hi there, thank you for your reply.

I tried as you suggested and oddly enough proved part B. I don't understand why though, in part a the force of the springs should be summed because there in the same direction where as in part b they should be subtracted because there in opposite direction.

[PLAIN]http://img262.imageshack.us/img262/3219/lastscanmz.jpg
 
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  • #4
Matt1234 said:
I tried as you suggested and oddly enough proved part B. I don't understand why though, in part a the force of the springs should be summed because there in the same direction where as in part b they should be subtracted because there in opposite direction.
In part a each spring has the same tension, since they are in series (and presumably massless). You'll need to use that fact to figure out the effective spring constant for springs in series.

In part b, when the mass moves to the right (for example) both springs exert a force on it to the left. So the net force on the mass is the sum of the forces of each spring.
 

1. What is SHM?

SHM stands for Simple Harmonic Motion. It is a type of periodic motion where an object oscillates back and forth around a central equilibrium point.

2. How are two springs and one mass related in SHM?

In SHM, two springs and one mass are often used as a model system to demonstrate periodic motion. The two springs are connected to the mass and the system is set into motion, causing the mass to oscillate back and forth between the two springs.

3. What factors affect the period of SHM?

The period of SHM is affected by three main factors: the mass of the object, the spring constant of the springs, and the amplitude (maximum displacement) of the motion. A heavier mass, stiffer springs, and larger amplitude will result in a longer period.

4. How is the period of SHM calculated?

The period of SHM can be calculated using the equation T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. This equation assumes that the amplitude is small.

5. What is the relationship between SHM and energy conservation?

In SHM, energy is conserved between kinetic energy and potential energy. As the mass oscillates back and forth, the energy is constantly being transferred between these two forms, but the total energy remains constant.

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