Three spring are connected to a mass `m(=100g)` as shown in figure. Given `k=2.5Nm^(-1)`. (a) What is the effecitve spring constant of the combination of spring constant of the combination of springs? (b) When mass m oscillates, find time period of its vibration.

Explanation

(a) In the given combination of springs, three springs of spring constant, 2k, k and k are in parallel, their effective spring constant K is
`K=2k+k+k=4k=4xx2.5=10Nm^(-1)`
(b) Time period of oscillation,
`T=2pisqrt((m)/(K))=2pisqrt((0.100)/(10))`
`=2xx(22)/(7)xx(1)/(10)=0.628s`