Figure shows the system of two springs which is in oscillatory motion due to Force F.
Let the spring constant of spring-1 be k1 and its amplitude be A1 .
Similarly the spring constant of spring-2 be k2 and its amplitude be A2 .
net Amplitde A = A1 + A2...............(1)
When displacement is maximum, force acting on each spring is shown in figure.
internal restoring forces acting in spring-2 is k2A2 . Restoring force acting in spring-2 pulls spring-1 .
Since restoring force acting in spring-1 is k1A1 , at the time of maximum displacement,
k1A1 = k2A2 ...................(2)
Using eqn.(1), we write eqn.(2) as, k1A1 = k2 ( A - A1)
Hence from above eqn., we get , A1 = [ k2 / (k1 + k2) ] A