Question

The dynamic equation of motion of a structure contains M, C and K as mass, damping and stiffness matrices of the structure, respectively. If F is an external load vector, then which option is correct about the equation?

(a) M\(\ddot{x}\) + K\(\dot{x}\) + Cx = F

(b) M\(\ddot{x}\) is time-dependent

(c) All the forces are time-independent

(d) The equation is of 3^rd order

I got this question in a national level competition.

My enquiry is from Eigen Value and Time Dependent Problems in section Single Variable Problems of Finite Element Method

Answer 1

The correct option is (b) M\(\ddot{x}\) is time-dependent

To elaborate: The dynamic equation of motion of a structure is a 2^nd order equation. It is written as M\(\ddot{x}\) + C\(\dot{x}\) + Kx = F, where M, C and K are the mass, damping and stiffness matrices of structure, respectively. All the forces in the equation are time-dependent. M\(\ddot{x}\) is inertia force, Kx is spring force, and C\(\ddot{x}\) is damping force.