A massless rod with length L is
attached to two springs at its two masses (both m) at its two ends.
The masses are connected to springs. The springs can move in the
horizontal and vertical directions as shown in the figure and they
both have a stiffness k. Note that gravity acts. Assume the springs
are un-stretched when the rod is vertical. Find the equation of
motion for the system using 1. Newton’s second law 2. Conservation
of energy. Please be as thorough as possible I do really want to
learn this.
Homework Answers
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A massless rod with length L is
attached to two springs at its two masses (both...
Consider two masses, both with mass M, attached to a spring with spring constant k. They...
Consider two masses, both with mass M, attached to a spring with
spring constant k. They slide along angled rails, and the angle
between the rails is theta. There is no friction: the masses slide
freely along the rails. Assume that the masses move together so
that the spring remains parallel to its equilibrium position. The
masses are initially moving upwards such that the spring is being
stretched past its equilibrium length. Describe what happens next,
by using Newton's second...
2) A particle of mass m, is attached to a massless rod of length L which...
2) A particle of mass m, is attached to a massless rod of length L which is pivoted at O and is free to rotate in the vertical plane as shown below. A bead of mass my is free to slide along the smooth rod under the action of a spring of stiffness k and unstretched length Lo. (a) Choose a complete and independent set of generalized coordinates. (b) Derive the governing equations of motion. m2
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A massless rod of length l has weights, each of mass m, attached to its ends. The rod is initially put in a horizontal position, and laid on an off-center fulcrum located at a distance b from the rod’s center. The rod will topple. a) Calculate the total gravitational torque on the rod directly, by adding the two torques. b) Verify that this gives the same result as would have been obtained by taking the entire gravitational force as acting...
Two equal masses of 3.0 kg are at the ends of a 90-cm-long massless rod. The...
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The figure shows a long, nonconducting, massless rod of length L, pivoted at its center and...
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5. 10 points Two ideal massless springs with spring constant k are connected to two masses that hang vertically as shown in the figure. The top one has mass 3m and the bottom one has mass 2m. The system is only able to oscillate in the vertical direction. a) Determine the equations of motion. (4 pts) b) Find the frequencies of the normal modes of this system for small vertical dis- placements. (4 pts) c) Describe the relative motion and...
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Problem 1: Axial vibrations of a rod The rod of length L is fixed at ends x = 0 and x = L. The density of the rod is ρ(x), stiffness k(x) being subjected to a force f(x, t). Let's derive the equations for axial vibrations of a rod using almped model. We express the rod niy mol 41 in as a chain of masses m,mm, connected to each other through springs as shown in the figure. Let's say each...
4. Two objects of masses m/ and m2 are connected by a massless spring as shown...
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Two objects are attached with a massless string over a massless, frictionless pulley as shown below....
Two objects are attached with a massless string over a massless, frictionless pulley as shown below. The horizontal surface is frictionless. Draw the free body diagrams for the masses. Include the assumed directions for the accelerations of the masses. Write down the expressions from Newton's 2nd Law for the two masses. Clearly indicate the coordinate systems used for each mass. Determine the acceleration of the masses.
NEED ASAP A pendulum is made up of a massless rod of length 1.6 m attached...
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Consider two masses, both with mass M, attached to a spring with
spring constant k. They slide along angled rails, and the angle
between the rails is theta. There is no friction: the masses slide
freely along the rails. Assume that the masses move together so
that the spring remains parallel to its equilibrium position. The
masses are initially moving upwards such that the spring is being
stretched past its equilibrium length. Describe what happens next,
by using Newton's second...
2) A particle of mass m, is attached to a massless rod of length L which is pivoted at O and is free to rotate in the vertical plane as shown below. A bead of mass my is free to slide along the smooth rod under the action of a spring of stiffness k and unstretched length Lo. (a) Choose a complete and independent set of generalized coordinates. (b) Derive the governing equations of motion. m2
Two equal masses of 3.0 kg are at the ends of a 90-cm-long massless rod. The rod spins at 7.0 rev/s about an axis through its center of mass. Suddenly, a compressed gas expands the rod out to a length of 180 cm. What is the rotation frequency after the expansion? (rev/sec is frequency)( use conservation of angular momentum.)
The figure shows a long, nonconducting, massless rod of length L, pivoted at its center and balanced with a block of weight W at a distance x from the left end. At the left and right ends of the rod are attached small conducting spheres with positive charges q and 2q, respectively. A distance h directly beneath each of these spheres is a fixed sphere with positive charge Q. (a) Find equation for the distance x when the rod is...
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