Consider a machine of mass 70 kg mounted to ground through an isolation system of total stiffness 30,000 n> m, with a measured damping ratio of 0.2. the machine produces a harmonic force of 450 n at 13 rad> s during steady-state operating conditions. determine (a) the amplitude of motion of the machine, (b) the phase shift of the motion (with respect to a zero phase exciting force), (c) the transmissibility ratio, (d) the maximum dynamic force transmitted to the floor, and (e) the maximum velocity of the machine.

a)0.0229 m

b)0.393 rad

c)1.57

d)707.6 N

e)0.298 m/s

Explanation:

Given:

a)We know that the amplitude X at steady state is given by

Where

b) The phase shift of the motion is given by

c)Transmissibility ratio is given by

d)The magnitude of the force transmitted to the ground is

e)The maximum velocity is given by

i think it because equal matrices have equal dimensions, only square matrices can be symmetric. for all indices and . every square diagonal matrix is symmetric, since all off-diagonal elements are zero. in linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space.

the inner core.

good luck: )

klicker