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### Effective spring mass constant

Posted: **Fri Jan 19, 2007 2:26 pm**

by **seba240698**

In the study of Simple Harmonic Motion, one always come across questions on combine (usually 2) springs.

May I know what is the effective spring constants of 2 springs when they are:-

a) joined in parallel,

b) joined in series?

Thanks.

Posted: **Fri Jan 19, 2007 3:08 pm**

by **CPT**

a) k_1 + k_2

b) (k_1 k_2) / (k_1 + k_2)

This is pretty trivial to see for yourself actually :

a> In this case both springs will exert force, and if the displacement is x, then F = F_1 + F_2 = k_1x + k_2 x = (k_1 + k_2)x

b> In this case the strectch in both the sprngs is different, say x_1 & x_2, but the tension (or compression) in the two springs must match, and this is the force that will be passed on to the block.

Therefore: k_1 x_1 = k_2 x_2 = k' x;

& x_1 + x_2 = x

So: 1/k' = x/(k' x) = (x_1 + x_2)/ (k'x) = x_1/ (k' x) + x_2/(k' x) = x_1/ (k_1x_1) + x_2/(k_2 x_2) = 1/k_1 + 1/k_2

Hope that helps

Posted: **Sun Jan 21, 2007 10:35 am**

by **seba240698**

Thanks, CPT.

I guess this is too trival to be listed in many undrgraduate textbooks, that was why I couldn't find it.