The period of oscillation of mass M suspended from a spring of negligible mass is T. If along with it another mass M is also suspended, the period of oscillation will now be

Options

A. T
B. `(T)/(sqrt(2))`
C. 2T
D. `sqrt(2)T`

Answer

D

Explanation

A mass M is suspended from a massless spring of spring constant k as shown in figure (a). Then,
Tim period of oscillation is `T=2pisqrt((M)/(k))" "...(i)`
When a another mass M is also suspended with it as shown in figure (b). Then,
Time period of oscillation is
`T.=2pisqrt((M+M)/(k))`
`=2pisqrt((2M)/(k))`
`=sqrt(2)(2pi.sqrt((M)/(k)))=sqrt(2)T` (Using (i))