BITSAT 2017 Slot 2 Solved Paper

From the conservation principle,
mgh=frac‌1‌2‌k‌X02−mgX0
where, X0 is maximum elongation in spring.
⇒

1

2

kX02−mgX0−mgh=0
⇒X02−

2mg

k

X0−

2mg

k

h=0
X0=

2 mg 2 ±√( 2mg k )2+4× 2mg k h

2

Amplitude = elongation in spring for lowest extreme position- elongation in spring for equilibrium position
=X0−X1=

mg

k

√1+

2hk

mg

‌‌‌‌[∵X1=

mg

k

]