16.6 For the spring-mass system shown in Figure P166, determine the mass displacement,velocity, and acceleration for ve time steps using (a) the central difference method,(b) Newmarks time integration method, and (c) Wilsons method. Let k 1200 lb/ftand m 2 slugs.

Figure P166

16.7 For the bar shown in Figure P167, determine the nodal displacements, velocities,and accelerations for ve time steps using two nite elements. Let E 30 106 psi,r 0:00073 lb-s2/in4, A 1 in2, and L 100 in.

Figure P167

16.8 For the bar shown in Figure P168, determine the nodal displacements, velocities,and accelerations for ve time steps using two nite elements. For simplicity of cal-culations, let E 1 106 psi, r 1 lb-s2/in4, A 1 in2, and L 100 in. UseNewmarks method and Wilsons method.

Figure P168

704 d 16 Structural Dynamics and Time-Dependent Heat Transfer