3. Consider the system shown in Figure 2. Write down the equation of motion and comment...
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.
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
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
012) Write the equation of motion if the system is undamped as shown above and derive the displacement response of the system if P(t) is given as in Figure 2. (4 Points) P(t) Po 2t Figure 2: P(t) force as a function of time 012) Write the equation of motion if the system is undamped as shown above and derive the displacement response of the system if P(t) is given as in Figure 2. (4 Points) P(t) Po 2t Figure...
2. Consider the mass-spring system shown in the figure below. It can be shown that the motion of the mass is governed by the equation a=-sw^2, where s and a are the position and acceleration of the mass, respectively, and w is a constant (which is referred to as the natural frequency of the system). Derive the equation describing the velocity of the mass in terms of the position. Assume that the velocity of the mass is v(subzero) when s=0...
(5 marks) Write the equation of motion for the double pendulum system shown below. Assume that the displacement angles of the pendulum are small enough to ensure that the spring is always horizontal. The pendulum rods are taken to be massless, of length I, and the springs are 75% of the way down the rods. 3. k, m2
An automobile suspension system is modeled as a 2-DoF vibration system as shown in Figure below Derive the equation of motion Determine the natural frequencies of the automobile with the following data Mass (mm) = 1000kg1000kg Momen of inertia (ImIm) = 450kgm2450kgm2 Distance between front axle and C.G. (LfLf) = 1.2m1.2m Distance between rear axle and C.G. (LfLf) = 1.5m1.5m Front spring stiffnes (kfkf) = 18kN/m18kN/m Rear spring stiffnes (krkr) = 17kN/m17kN/m Front damper coefficient (cfcf) = 3kNs/m3kNs/m Rear damper...
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...
8. Write down the state space equation for the system shown below US) + 2 y(s) $+3 2 s(s+1) 9. Derive the state space equation for the system shown where the coefficients of the system matrix are in diagonal form and the elements of the control matrix are unity. U(S) 1 X2 $+2 X 3+1 X = y $+3 $+4 S
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