Question

A block of mass $m$, attached to a 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. $x=\sqrt{mv/k}$

Answer 1

Answer: (C)

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

By using conservation of mechanical energy
$\frac{1}{2}k{x}^2=\frac{1}{2}m{v}^2$

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