A Block of mass 'm' are kept on a smooth horizontal plane, and attached to two unstretched spring with spring constants $k_1$ and $k_2$ as shown. If the block be displaced by a distance x on either side and released then the velocity of block as it passes through the mean position is

Question

$ a)\; x \sqrt {\large\frac{m}{k_1}+\frac{m}{k_2}} \\ b)\; x \sqrt {\large\frac{k_1k_2}{m(k_1+k_2)}} \\ c)\; x \sqrt {\large\frac{k_1+k_2}{m}} \\ d) zero $

Answer 1

Spring $k_1$ is compressed, and $k_2$ expanded by distance x

Using conservation of energy

the total potential energy of the spring= Kinetic energy of the mass

$\large\frac{1}{2}$$k_2x^2+\large\frac{1}{2}$$k_1x^2=\large\frac{1}{2}$$mv^2$

$v=x \sqrt {\large\frac{k_1+k_2}{m}}$

Hence  cis the correct answer.