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

[Matt1234]

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.

 

[Doc Al]

Use Hooke's law to figure out the effective spring constant in each case.

 

[Matt1234]

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

 

[Doc Al]

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.

 

[Matt1234]

thank you, so far i got part a. For other with a similar problem this site is useful:
http://scienceworld.wolfram.com/physics/SpringsTwoSpringsinSeries.html