What is the equation for the period of two equal springs in parallel?
In series?

The two equations I have been give are: 

T^2 = T1^2 + T2^2
 and 
1/T^2 = (1/T1^2) + (1/T2^2)

I just don't know which is the series equation and which is the parallel equation.

Please provide a derivation or proof.

Note: I don't need the spring constant formulas--I need the period formulas.

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Request for Question Clarification by hedgie-ga on 27 Nov 2005 18:46 PST

Sorry,
but springs do not have periods. They only have spring constants.

Spring combined with a mass forms an oscilator. 
Oscilator has a period which depends on spring constant and the mass.

If you have two masses and and two springs, the meaning of 'series'
is ambiguous. You may have to provide a picture or better description.

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Request for Question Clarification by livioflores-ga on 27 Nov 2005 19:20 PST

Hi!!

As my fellow researcher hedgie-ga tolds you, period is a property of
an oscilator which is the combination of an spring with constant k and
a mass m attached to it.
Taking this into account let me know if the following page answers your question:
"Springs":
http://online.cctt.org/physicslab/content/PhyAPB/lessonnotes/springs/lessonsprings.asp

As you can see there is a relationship between constants in series and
parallel springs. The resultant k must be plugged into the period
formula to calculate it, and there is no a relationship between
periods, at least not a useful one.

See also:
"Springs--Two Springs in Series -- from Eric Weisstein's World of Physics":
http://scienceworld.wolfram.com/physics/SpringsTwoSpringsinSeries.html

"Springs--Two Springs in Parallel -- from Eric Weisstein's World of Physics":
http://scienceworld.wolfram.com/physics/SpringsTwoSpringsinParallel.html


Please let me know if this answers your question so I can claim the
prize by posting this in the answer box.

Regards,
livioflores-ga

this sounds like homework, so I won't give a detailed derivation.

As mentioned above, to solve this simple harmonic oscillator problem
(1) find the force constants and (2) use the force constants in the
period formula (hint: it also contains mass m and the factor 2 pi).

(1) The force constants can be found by a quick google search (spring
constant series parallel), or by the links listed above.  Use F=-kx,
for the parallel case the F add together and all the x are the same
(meaning k=k1+k2); for series the x add together and all F are the
same (meaning 1/k=1/k1+1/k2).

(2) Use T=2pi*sqrt(m/k).  Contrary to one of the clarification notes
there are simple results as correctly given in your question.  Try
calculating T^2 and 1/T^2 and you should be able to derive the right
answer.

If you're still stuck I can tell you which one is which.

Just came across this interesting problem. For two springs in
parallel, the answers are all correct, k=k1+k2. For two springs in
series, all gave the same answer,  1/k = 1/k1 + 1/k2, which is WRONG!
Why? because if k1=k2, we will get 1/k=2/k1 which is obviously wrong
because in this case you have effectively only a single spring. The
correct answer should be: 2/k=(1/k1+1/k2).

The derivation in http://scienceworld.wolfram.com/physics/SpringsTwoSpringsinSeries.html
is also incorrect.