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

Answer 1

Answer: (C)

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

Answer 2

By using conservation of mechanical energy

$\frac { 1 } { 2 } k x ^ { 2 } = \frac { 1 } { 2 } m v ^ { 2 } \Rightarrow x = v \sqrt { m / k }$