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. $\frac{mg}{k}$
• B. $\frac{mg}{k}$ + $\left( \frac{2hk}{mg} \right)^{1/2}$
• C. mg $\sqrt{1 + \frac{1 + 2hk}{mg}}$
• D. $\frac { \mathrm { mg } } { \mathrm { k } }$ $\left\lbrack 1 + \sqrt{1 + \frac{2hk}{mg}} \right\rbrack$

Answer 1

Answer: (D)

\frac { \mathrm { mg } } { \mathrm { k } }$$\left\lbrack 1 + \sqrt{1 + \frac{2hk}{mg}} \right\rbrack

Answer 2

mg (h + x) = $\frac{1}{2}$kx² ⇒ x²–$\left( \frac{2mg}{k} \right)$x–$\frac{2mgh}{k}$ = 0

⇒ x = $\frac{mg}{k}$ + $\frac{mg}{k}$ $\left( 1 + \frac{2hk}{mg} \right)^{1/2}$