Prove that when two springs are attached one at the end of the other, the coefficient of the final spring becomes
1 / (1/k1 + 1/k2 ) where k1 and k2 are the coefficient of the two individual springs.
Then consider two systems of springs, one in which a mass m is attached two the end of two springs which are placed one at the end of the other, another in which m is attached to the two springs in parallel (each spring has coefficient respectively k1 and k2)
Find the frequency of oscillations of mass m in the two cases
Here is the strategy to solve this problem:
The key point is that when the springs are connected in series and stretched (or compressed) the both exert the same force.
Write down the force each spring exerts (take their displacement from equilibrium lengths as x1 and x2)and equate them.
Express x1 as a function of x2,k1 and ...
The solution describes how to calculate the effective spring constant of two springs connected in either parallel or in series.