The mass M shown in the figures oscillate in SHM motion with amplitude A. The amplitude of point P is

Let the spring constant of spring-1 be k1and its amplitude be A1.
Similarly the spring constant of spring-2 be k2and 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