Springs of spring constants k, 2k, 4k, 8k, …… are connected in series. A mass m kg is attached to the lower end of the last spring and the systemm is allowed to vibrate. What is the time period of oscillations? Given `m=40gm,k=2.0Ncm^(-1)`.

Options

A. 1 s
B. 0.1256 s
C. 0.5 s
D. 3.142 s

Answer

B

Explanation

The effective spring constant k.
By using Geometric progression is given by
`(1)/(k_(s))=(1)/(k)+(1)/(2k)+(1)/(4k)+(1)/(8k)+....`
`=(1)/(k)[1+(1)/(2)+(1)/(4)+(1)/(8)+....]=(1)/(k)[(1)/(1-(1//2))]`
`(1)/(k_(s))=(2)/(k) therefore k_(s)=(k)/(2)`
`T=2pisqrt((m)/(k))=2pisqrt((m)/(k//2))=2pisqrt((2m)/(k))`
`=2pisqrt((2xx0.04)/(2xx100))=0.1256s`