Three springs are connected to a mass m as shown in figure, When mass oscillates, what is the effective spring constant and time period of vibration? Given `k=2Nm^(-1)` and m=80 gram.

Options

A. `8Nm^(-1), 0.628s`
B. `6Nm^(-1), 0.628s`
C. `8Nm^(-1), 0.526s`
D. `6Nm^(-1), 0.526s`

Answer

A

Explanation

Here,`m=80gram=0.08kkg, k=2Nm^(-1)`
The equivalent arrangement of spring system is shown in figure. This show that all the springs are connected in paralledl.
`:.` effective spring constant
`K=k+2k+k=4k=4xx2=8Nm^(-1)`
Time period `=2pisqrt((i n ertia fact o r )/(spri ng fact o r))=2pisqrt((m)/(4k))`
`=2pisqrt((0.08)/(8))=0.628s`