Two springs are connected to a block of mass M is placed on a frictionless surface as shown in figure. If both springs have a spring constant k, the frequency of oscillation of the block is………

Options

A. `(1)/(2pi) sqrt((k)/(M))`
B. `(1)/(2pi) sqrt((k)/(2M))`
C. `(1)/(2pi) sqrt((2k)/(M))`
D. `(1)/(2pi) sqrt((M)/(k))`

Answer

B

Explanation

The spring constant of spring constanted in series `k. = (k_(1)k_(2))/(k_(1)+k_(2))`,
`k.= ((k)(k))/(k+k)= (k)/(2)`
The resultant frequency,
`f= (1)/(2pi) sqrt((k.)/(M))= (1)/(2pi) sqrt((k)/(2M))`.