According to energy conservation principle, If, x1 is maximum elongation in the spring when the particle is in its lowest extreme position. Then, mgh =
1
2
kx12 - mgx1 ⇒
1
2
kx12−mgx1 - mgh = 0 or x12 -
2mg
k
x1−
2mg
k
h = 0 ∴ x1 =
2mg
k
±√[(
2mg
k
)2+4×
2mg
k
h]
2
Amplitude A = X1–X0 (elongation in spring for equilibrium position) A =