Figure. (a) shows a spring of force constant k fixed at one end and carrying a mass m at the other end placed on a horizontal frictionless surface. The spring is stretched by a force F. Figure. (b) shows the same spring with both endsf free and a mass m fixed at each free end Each of the spring is streched by the same force F. The mass in case (a) and the masses in case (b) are then released. Which of the following statements are true?

Options

A. While oscillating, the maximum extension of the spring is more in case (a) then in case (b)
B. The maximum extension of the spring is same in both cases.
C. The time period of oscillation is the same in both cases.
D. The time period of oscillation in case (a) is `sqrt(2)` times that in case (b).

Answer

B, D

Explanation

Extension, `x = F//k`, as `F` is same in both cases,
`x` will be same. Time period `= 2pi sqrt((m)/(k))`
`rArr (T')/(T) = sqrt((k)/(k')) = sqrt((1)/(2)) = (1)/(sqrt(2))`