A block of mass `m` is suspended from a spring and executes vertical SHM of time period T as shown in Fig. The amplitude of the SHM is A and spring is never in compressed state during the oscillation. The magnitude of minimum force exerted by spring on the block is

Options

A. `mg-(4pi^2)/(T^2)mA`
B. `mg+(4pi^2)/(T^2)mA`
C. `mg-(pi^2)/(T^2)mA`
D. `mg+(pi^2)/(T^2)mA`

Answer

A

Explanation

The spring is never compressed. Hence spring shall exert least force on the block when the block is at topmost position. At equilibrium positon `kx_0=mgimpliesx_0=(mg)/(k)`.
`F_(max)=k(x_0-A)=k[(mg)/(k)-A]`
`=mg-4(pi^2)/(T^2)mA=mg-kA=mg-momega^2A`