two subway cars as shown in Figure 1 have mass m = 2000 kg and are...

two subway cars as shown in Figure 1 have mass m = 2000 kg and are connected by a coupler that can be modeled as a spring of stiffness k = 280,000 N/m. Use Newton’s method to derive the equations of motion, calculate the natural frequencies and determine the associated mode shapes. also, find the time response x1(t) and x2(t) of the subway initial conditions: x(0)= [ 0, 0.2] with zero initial velocity vector.

Solutions

Expert Solution

samet mamat answered 1 year ago

Next > < Previous

Related Solutions

Two cars collide at an intersection. Car A, with a mass of 2000 kg , is...

Two cars collide at an intersection. Car A, with a mass of 2000 kg , is going from west to east, while car B, of mass 1400 kg , is going from north to south at 14.0 m/s . As a result of this collision, the two cars become enmeshed and move as one afterwards. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of...

Two cars collide at an intersection. Car A, with a mass of 2000 kg , is...

Two cars collide at an intersection. Car A, with a mass of 2000 kg , is going from west to east, while car B, of mass 1300 kg , is going from north to south at 17.0 m/s . As a result of this collision, the two cars become enmeshed and move as one afterwards. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of...

As shown in the figure below, a box of mass m = 68.0 kg (initially at...

As shown in the figure below, a box of mass m = 68.0 kg (initially at rest) is pushed a distance d = 91.0 m across a rough warehouse floor by an applied force of FA = 226 N directed at an angle of 30.0° below the horizontal. The coefficient of kinetic friction between the floor and the box is 0.100. Determine the following. (For parts (a) through (d), give your answer to the nearest multiple of 10.) (d) work...

As shown in the figure, a conducting rod with a linear mass density of 0.0395 kg/m...

As shown in the figure, a conducting rod with a linear mass density of 0.0395 kg/m is suspended by two flexible wires of negligible mass in a uniform magnetic field directed into the page. A power supply is used to send a current through the rod such that the tension in the support wires is zero. (a) If the magnitude of the magnetic field is 3.70 T, determine the current in the conducting rod. (b) Determine the direction of the...

As shown in the figure (Figure 1) , a superball with mass m equal to 50...

As shown in the figure (Figure 1) , a superball with mass m equal to 50 grams is dropped from a height of hi=1.5m . It collides with a table, then bounces up to a height of hf=1.0m . The duration of the collision (the time during which the superball is in contact with the table) is tc=15ms . In this problem, take the positive y direction to be upward, and use g=9.8m/s2 for the magnitude of the acceleration due to...

In the figure, two particles, each with mass m = 0.77 kg, are fastened to each...

In the figure, two particles, each with mass m = 0.77 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.2 cm and mass M = 1.0 kg. The combination rotates around the rotation axis with angular speed ? = 0.32 rad/s. Measured about O, what is the combination's (a) rotational inertia and (b) kinetic energy?

E3. A block of mass 1.00 kg sits on an inclined plane as shown. (Figure 1)A...

E3. A block of mass 1.00 kg sits on an inclined plane as shown. (Figure 1)A force of magnitude 50.0 N is pulling the block up the incline. The coefficient of kinetic friction between the plane and the block is 0.500. The inclined plane makes an angle 10.0 degrees with the horizontal. What is the total work Wfric done on the block by the force of friction as the block moves a distance 6.00 mm down the incline? E12. On...

1.) In the figure, a block of mass m = 13 kg is released from rest...

1.) In the figure, a block of mass m = 13 kg is released from rest on a frictionless incline of angle θ = 30°. Below the block is a spring that can be compressed 3.7 cm by a force of 210 N. The block momentarily stops when it compresses the spring by 6.0 cm. (a) How far does the block move down the incline from its rest position to this stopping point? (b) What is the speed of the...

(a) A block of mass m = 3.90 kg is suspended as shown in the diagram...

(a) A block of mass m = 3.90 kg is suspended as shown in the diagram below. Assume the pulley to be frictionless and the mass of the strings to be negligible. If the system is in equilibrium, what will be the reading of the spring scale in newtons? N (b) Two blocks each of mass m = 3.90 kg are connected as shown in the diagram below. Assume the pulley to be frictionless and the mass of the strings...

Boxcar #1 has a mass of 2000 kg. Boxcar #2 has a mass of 1200 kg....

Boxcar #1 has a mass of 2000 kg. Boxcar #2 has a mass of 1200 kg. Boxcar #1 is moving at 12.00 m/s to the right before they hit and stick together. A) Suppose that the velocity of Boxcar #2 before the collision is 8.00 m/s to the right. What is the velocity after the totally inelastic collision? B) Suppose, instead, that the speed after the totally inelastic collision is 3.00 m/s. What was the velocity of Boxcar #2 before...

Subjects