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Q. The resultant spring constant of the system of springs shown belowPhysics Question Image

KEAMKEAM 2005Oscillations

Solution:

The first two springs are in paralleI, so their equivalent spring constant
$ \, \, \, \, \, \, \, \, k'=k_1+k_2$
Now, this combination is in series with the third spring, so their equivaient spring constant
$ \, \, \, \, \, \, \, \, k=\frac{k' \times k_3}{k'+k_3}$
$ \, \, \, \, \, \, \, \, \, \, \, =\frac{(k_1+k_2)(k_3)}{k_1+k_2+k_3}$