5. Find the equation of motion of the system shown in Figure Q.5 assuming that the...
For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3-0 (the upper end is fixed and K1 and K2=K (5) Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes Determine and explain how to get the natural frequencies 1. (5) (5) 2. 3. Figure 5 ww ww-
For the system shown in Figure 5, a. How many degrees of freedom...
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.
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.
1 Q2. Figure 2 shows a system in which mass m is connected with a cylinder of mass m2 and moment of inertia Jo through a horizontal spring k. The cylinder is m1 rolling on the rough surface without slipping. (1) Find its total kinetic energy, total potential energy TN and Lagrangian, Figure 2 (2) Derive the equations of motion using Lagrangian equation method, and (3) Calculate its natural frequencies
1 Q2. Figure 2 shows a system in which mass...
Problem 1 - Combined Systems (30pts) Consider the system shown in Figure 1 and assume that: The wheel rolls without slipping on the mass M2 The block M2 is able to slide without friction on the horizontal surface. There is external torque τ(t) is applied on the wheel that drives the whole system. x1(t) r2(t) M2 t(0) Figure1 Draw the free body diagram clearly indicating forces and coordinate system. Derive the equation of motion of the system as function of...
Problem 5 (20%) For the system shown in Figure 5, a. How many degrees of freedom is this system and why? (5) b. If x3 0 (the upper end is fixed and K1 and K2=K Write the equations of motion. Set the necessary matrix to find the natural frequencies and mode shapes (5) (5) (5) 1. 2. 3. Determine and explain how to get the natural frequencies. m2 Figure 5 www
Problem 5 (20%) For the system shown in Figure...
Problem 2) The cord passes over a frictionless bend, as shown in the figure, carrying = 40 kg at one end and wrapped around a cylinder of mass M2 50 kg that rolls without slipping on the horizontal surface. The system is released, find the a mass M1 acceleration of mass M1. Hint: Note that the acceleration of the cord on the top of the cylinder is twice the acceleration of the center of the cylinder]
Problem 2) The cord...
The undamped pendulum pivoted at point O shown in Figure E3.48
has a cylinder of mass m2 at its top that rotates without slipping
on the interior of a cylinder. At the bottom end of the pendulum, a
mass m1 is attached. The rod connecting the two masses is rigid and
weightless. The system is in equilibrium at theta = 0. Determine an
expression for the
period of oscillation of the system. Assume that m2L2 < m1L1.
(Using Lagrange's method)...
Question 2 (Combinatorial system). For the system shown in Figure 2, the disk rolls without slipping, the masses of the pulleys are negligible, and the cable is inextensible. The coordinates are defined relative to the static equilibrium position of the system. Derive the equation of motion in terms of y (mass position). X WWW Figure 2: Rotational / translational system.
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...