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

Answer 1

Answer: (C)

By energy conservation,
When the spring is at its natural length, the velocity of the block is maximum i.e $u$
The total Kinetic energy is converted to the elastic potential energy of the spring.
$\Rightarrow \frac{1}{2}mu^{2}=\frac{1}{2}Kx^{2}\Rightarrow mu^{2}=Kx^{2}\Rightarrow x=u\sqrt{\frac{m}{K}}$