A particle of mass 'm' is attached to three identical springs `A,B` and `C` each of force constant 'K' as shown in figure. If the particle of mass 'm' is pushed slightly against the spring 'A' and released the period of oscillations is

Options

A. `T = 2pi sqrt((m)/(K))`
B. `T = 2pi sqrt((2m)/(K))`
C. `T = 2pi sqrt((m)/(2K))`
D. `T = pi sqrt((m)/(K))`

Answer

C

Explanation

Net restoring force `= k_(2) x + 2 (k_(1)x cos theta) cos theta`
`m omega^(2)x = (k_(2) + 2k_(1)cos^(2) theta)x`
`T = 2pi sqrt((m)/(k_(2) + 2k_(1) cos^(2) theta))`