Question

A solid ball of mass m is allowed to fall from a height h to a pan suspended with a spring of spring constant k. Assume the ball does not rebound and pan is massless, then amplitude of the oscillation is

• A. $\frac { m g } { k }$
• B. $\frac { m g } { k } + \left( \frac { 2 h k } { m g } \right) ^ { 1 / 2 }$
• C. $m g \sqrt { 1 + \frac { 1 + 2 h k } { m g } }$
• D. $\frac { m g } { k } \left[ 1 + \sqrt { 1 + \frac { 2 h k } { m g } } \right]$

Answer 1

Answer: (D)

$\frac { m g } { k } \left[ 1 + \sqrt { 1 + \frac { 2 h k } { m g } } \right]$

Answer 2

mg (h + x) =-$\frac { 1 } { 2 }$ kx²

or x²-$\left( \frac { 2 m g } { k } \right) x - \frac { 2 m g h } { k }$ = 0

or x =$\frac { m g } { k } + \frac { m g } { k } \sqrt { 1 + \frac { 2 h k } { m g } }$