6 A 10 kg mass stretches a spring 25 m at equilibrium For wh

6. A 10 kg mass stretches a spring 2.5 m at equilibrium. For what values of the dampening constant c will a free vibration of the mass have infinitely many oscillations? You may assume that the constant of gravity is g = 10 m/s 2 .

Solution

Force = Mass*Acceleration.........(1)

F = m*a

In a case of spring

Force = Spring Dampening Constant * Displacement.......(2)

F = C*x

Equating both equations

m*a = C*x

10*10 = C*2.5

C = 100/2.5

C = 40 Kg/s²