VW It 2 Assume that the mass and stiffness of the system sho

VW It 2. Assume that the mass and stiffness of the system shown above are m 5 k.s2/in and k= 20 kin, and that it is undamped. If the initial displacement is 1.8 in, and the displacement at t= 1.2 s is also 1.8 in, determine: a. the displace ment at t 2.4 s the amplitude of free vibration,

Solution

Solution:-

                       = (K/M)

                            = (20/5) = 2 radian/second

u₀ = 1.8 inch

u = u₀cos (t) + u₀’/ x sin (t)  

    1.8= 1.8 cos (2 x1.2) + u₀’/2 x sin (2 x1.2)

_u0’ = 0.075 inch/second

At   t = 2.4

u =1.8 cos (2 x2.4) + 0.075/2 x sin (2 x2.4)

Displacement u = 1.79 inch

(b) Amplitude =(u₀² + (u₀/)²)

                     = ( (1.8)² + (0.075/2)²)

                      = 1.8 inch

When system is undamped then

p (damping ratio) =0