Consider the situation shown in figure. Show that if the blocks are displaced slightly in opposite directions and released, they will execute simple harmonic motion. Calculate the time period.

Options

A. `2pisqrt((m)/(k))`
B. `2pisqrt((m)/(2k))`
C. `2pisqrt((m)/(4k))`
D. `2pisqrt((2m)/(k))`

Answer

B

Explanation

Reduced mass of the system
`mu=((m)(m))/(m+m)=(m)/(2)`
`therefore`Time period, `T=2pisqrt((mu)/(k))=2pisqrt((m)/(2k))`