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# Spring System - SHM

My physics book covers SHM, and as an example, shows how to calculate the period, T, of a pendulum, a spring system, etc..

Now, with the spring system, an object of mass m is attached between TWO springs; one either side.

My book explains that the period for this system is 2*PI*sqrt(m/k).

And this is easy enough to derive..

But come to think about it, wouldn't that be the period for a system with only ONE spring?

..And when there are two (equal) springs, you would halve that value?

So shouldn't the period be: T=PI*sqrt(m/k) for the 2 spring example provided?

Now, with the spring system, an object of mass m is attached between TWO springs; one either side.

My book explains that the period for this system is 2*PI*sqrt(m/k).

And this is easy enough to derive..

But come to think about it, wouldn't that be the period for a system with only ONE spring?

..And when there are two (equal) springs, you would halve that value?

So shouldn't the period be: T=PI*sqrt(m/k) for the 2 spring example provided?

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The k in sqrt(m/k) represnts the total of all elastic forces acting on the mass

ASKER

So the two spring system would be smaller than a single spring system, by a factor of sqrt(2), right?

(that's taking both springs to be identical)

(that's taking both springs to be identical)

If by smaller you mean the period, and the springs are in parallel, yes.

If the springs are in series, then the frequency would be smaller

If the springs are in series, then the frequency would be smaller

ASKER

Thanks