Question

A block of mass m attached to a spring of spring constant k oscillates on a smooth horizontal table. The other end of the spring is fixed to a wall. The block has a speed v when the spring is at its natural length. Before coming to an instantaneous rest, if the block moves a distance x from the Mean position, then

• A. $x = \sqrt { m / k }$
• B. $x = \frac { 1 } { v } \sqrt { \frac { m } { k } }$
• C. $x = v \sqrt { m / k }$
• D. $x = \sqrt { m v / k }$

Answer 1

Answer: (C)

$x = v \sqrt { m / k }$

Answer 2

Kinetic energy of block $\left( \frac { 1 } { 2 } m v ^ { 2 } \right)$ = Elastic potential energy of spring $\left( \frac { 1 } { 2 } k x ^ { 2 } \right)$

By solving we get $x = v \sqrt { \frac { m } { k } }$ .