For the system shown in Figure P2.30, obtain the equation of motion in terms of x. Neglect the mass of the L-s...
In the pulley system shown in Figure P2.33, assume that the cable is massless and inextensible, and assume that the pulley masses are negligible. The force f is a known function of time. Derive the system's equation of motion in terms of the displacement. For the system shown in Figure P2.34, the solid cylinder of inertia I and mass m rolls without slipping. Neglect the pulley mass and obtain the equation of motion in terms of x.
Problem 2: (33pts.) The schematic shown below represents a model of a coin- operated amusement kiddie ride for young children. The ride consists of a cam- operated system in which the follower is modeled by the spring and dashpot shown. The input to the system is y(t) and its motion is given by the cam's geometry. Motion of the whale is obtained by the L-shaped connecting link connected to follower. The L-shaped linkage is considered a massless rigid L-arm. The...
02 Obtain the transfer function Y(s)yU(s) of the system shown in Figure. The vertical motion u at point P is the input. This system is a simplified version of an automobile or motorcycle suspension system. (In the figure mi and ki represent the wheel mass and tire stiffness, respectively.) Assume that the displacements x and y are measured from their respective equilibrium positions in the absence of the input u. Use Newton second law to derive the movement equations.
Write the equations of motion of the system shown in Figure P4.3, using Lagrange's equation. Write the equations in terms of x, and X. M Figure P4.3
Problem 4 Write the equation of motion of the system shown in Figure 3 using either Newton's law or the principle of conservation of energy. Pulley, mass moment of inertia J. x(1) Figure 3
4. Derive the equations of motion for the shown two degrees system in terms of x and ?. Bonus 12.5 Pts: Derive and solve the characteristic equation for l = 4 m, m = 3 kg, ki-1 N/m, and k2 = 2 N/m. .
Q5 The equation of the motion of the mechanical system shown in the following figure is governed by the following differential equation d2 x dx m7+9+= -f(t) - 3kx dt2 dt where m, C and k are mass, damping coefficient and spring constant, respectively. Consider the system with m = 10 kg, c = 80 Ns/m, k = 50 N/m, and the system is at rest at time t = 0 s. f(t) is the external force acting on the...
For the following systems derive the equation of motion in terms of the coordinates shown in the figure.
Write the differential equation of motion for the system shown in the figure, and find the damped natural frequency and damping ratio of this system.
5. Find the equation of motion of the system shown in Figure Q.5 assuming that the cylinder rotates without slipping. k2 X re ww m2, 10 Figure Q.5