A body of mass 0.4 kg is held between two massless springs whose ends are fixed to rigid walls as shown in the figure. The spring constants are 8 N/m and 2 N/m. If the body is displaced along the direction of the lengths of the springs and released, the time period (in second) of the oscillations will be (ignore vertical oscillation, if any )

Options

A. `2 pi`
B. `4 pi`
C. `0.2 pi`
D. `0.4 pi`

Answer

D

Explanation

The two springs are in parallel.
`therefore` The effective spring constant
`K=K_(1)+K_(2)=8+2=10 N//m`
`therefore T=2pi sqrt((m)/(K_(eff)))=2pi sqrt((0.4)/(10))=2pi sqrt((4)/(100))`
`=2pi xx(2)/(10)=0.4pi`