## Effective spring mass constant

seba240698
Posts: 14
Joined: Mon Dec 18, 2006 3:04 am

### Effective spring mass constant

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.

CPT
Posts: 77
Joined: Mon Jan 15, 2007 2:05 am
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

seba240698
Posts: 14
Joined: Mon Dec 18, 2006 3:04 am
Thanks, CPT.

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