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2) A particle of mass m, is attached to a massless rod of length L which...
2. Consider a particle of mass M attached to a rigid massless rod of fixed length...
2. Consider a particle of mass M attached to a rigid massless rod of fixed length R whose other end is fixed at the origin. The rod is free to rotate about its fixed point. (a) Give an argument why the Hamiltonian for the system may be written as 21 21 with/-MR2 (b) If the particle carries charge q, and the rotor is placed in a constant magnetic field B, what is the modified Hamiltonian? (e) What is the energy...
A mass m attached to the end of a massless rod of length L is free...
A mass m attached to the end of a massless rod of length L is free to swing below the plane of support, as shown in the figure above. The Hamiltonian for this system is given by 2 2 where θ and φ are defined as shown in the figure. On the basis of Hamilton's equations of motion, the gepsralized coordinate or momentum that isa constant in time is (A) 0 (B) ф (C) 0 (D) Pe (E) Po
Question 2 A particle of mass m, is attached to a spring of natural length 2le...
Question 2 A particle of mass m, is attached to a spring of natural length 2le and stiffness 2k, and a second spring of stiffness k and natural length lo. It lies on a smooth horizontal table. and the two spring ends are a fixed distance 4lo apart, as shown in Figure Q2. The particle is released from rest at a distance 2lo from each end. Let x be the distance of the particle from A wwwwwwwwww Figure 02 (a)...
A)How many degrees of freedom are there in the system? (b) Using appropriately-defined generaliz...
a)How many degrees of freedom are there in the
system?
(b) Using appropriately-defined generalized coordinates, find the
kinetic and potential
energies of the system.
(c) Write down the mass–inertia matrix for the system, and find the
configurations for
which the Lagrangian is not regular.
(d) Find the equations of motion for the system
A light nextensible rod OA of length is attached to the point O and free to rotate smoothly around that point. At the other end of the...
A massless rod with length L is attached to two springs at its two masses (both...
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....
1. A rod of length 3a is hinged at one end and supported by a spring of stiffness k at the other end. A mass m is attached 1/3 of the length from the hinge and a dashpot having a hinge. Ignore the ma...
1. A rod of length 3a is hinged at one end and supported by a spring of stiffness k at the other end. A mass m is attached 1/3 of the length from the hinge and a dashpot having a hinge. Ignore the mass of the rod, spring and damper (a) Derive the equation of motion for the system (101
1. A rod of length 3a is hinged at one end and supported by a spring of stiffness k at...
A rigid bar with mass m and length L is pivoted at the fixed point O....
A rigid bar with mass m and length L is pivoted at the fixed point O. A small disk of mass M is attached at the upper end of the bar. The disk is attached to a spring of stiffness k and a viscous damper with damping constant c. The moment of inertia of the bar about point O is Io M2/3 and the spring is unstretched when the bar is vertical. rs Under what condition is the vertical position...
A massless rigid rod whose length L = 21.0 cm has a ball of mass m...
A massless rigid rod whose length L = 21.0 cm has a ball of mass
m = 0.079 kg attached to one end (see Figure). The other end is
pivoted in such a way that the ball will move in a vertical circle.
The system is launched from the horizontal position A with an
initial downward speed v0. The ball just reaches point D
and then stops. Calculate v0.
What is the tension in the rod at B?
· Rod...
1) Consider a block of mass M connected through the massless rigid rod to the massless...
1) Consider a block of mass M connected through the massless rigid rod to the massless circular track of radius a on a frictionless horizontal table (see the Figure). A particle of mass m is constrained to move on the vertical circular track. The distance between the center of the circular track and the center of mass of the block of mass M is constant and equal to L. Assume that there is no friction between the track and the...
A bead of mass m slides without friction along a rod, one end of which is...
A bead of mass m slides without friction along a rod, one end of which is pivoted in such a way that the rod can be revolved about the z-axis at a constant angle a, as shown in Fig. 2. The rod is driven with constant angular velocity w about Oz. Use Lagrange method to derive the equation of motion for the bead. Use the distance of m from the origin as generalized coordinate and discuss the motion of the...
2. Consider a particle of mass M attached to a rigid massless rod of fixed length R whose other end is fixed at the origin. The rod is free to rotate about its fixed point. (a) Give an argument why the Hamiltonian for the system may be written as 21 21 with/-MR2 (b) If the particle carries charge q, and the rotor is placed in a constant magnetic field B, what is the modified Hamiltonian? (e) What is the energy...
A mass m attached to the end of a massless rod of length L is free to swing below the plane of support, as shown in the figure above. The Hamiltonian for this system is given by 2 2 where θ and φ are defined as shown in the figure. On the basis of Hamilton's equations of motion, the gepsralized coordinate or momentum that isa constant in time is (A) 0 (B) ф (C) 0 (D) Pe (E) Po
Question 2 A particle of mass m, is attached to a spring of natural length 2le and stiffness 2k, and a second spring of stiffness k and natural length lo. It lies on a smooth horizontal table. and the two spring ends are a fixed distance 4lo apart, as shown in Figure Q2. The particle is released from rest at a distance 2lo from each end. Let x be the distance of the particle from A wwwwwwwwww Figure 02 (a)...
a)How many degrees of freedom are there in the
system?
(b) Using appropriately-defined generalized coordinates, find the
kinetic and potential
energies of the system.
(c) Write down the mass–inertia matrix for the system, and find the
configurations for
which the Lagrangian is not regular.
(d) Find the equations of motion for the system
A light nextensible rod OA of length is attached to the point O and free to rotate smoothly around that point. At the other end of the...
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....
1. A rod of length 3a is hinged at one end and supported by a spring of stiffness k at the other end. A mass m is attached 1/3 of the length from the hinge and a dashpot having a hinge. Ignore the mass of the rod, spring and damper (a) Derive the equation of motion for the system (101
1. A rod of length 3a is hinged at one end and supported by a spring of stiffness k at...
A rigid bar with mass m and length L is pivoted at the fixed point O. A small disk of mass M is attached at the upper end of the bar. The disk is attached to a spring of stiffness k and a viscous damper with damping constant c. The moment of inertia of the bar about point O is Io M2/3 and the spring is unstretched when the bar is vertical. rs Under what condition is the vertical position...
A massless rigid rod whose length L = 21.0 cm has a ball of mass
m = 0.079 kg attached to one end (see Figure). The other end is
pivoted in such a way that the ball will move in a vertical circle.
The system is launched from the horizontal position A with an
initial downward speed v0. The ball just reaches point D
and then stops. Calculate v0.
What is the tension in the rod at B?
· Rod...
1) Consider a block of mass M connected through the massless rigid rod to the massless circular track of radius a on a frictionless horizontal table (see the Figure). A particle of mass m is constrained to move on the vertical circular track. The distance between the center of the circular track and the center of mass of the block of mass M is constant and equal to L. Assume that there is no friction between the track and the...
A bead of mass m slides without friction along a rod, one end of which is pivoted in such a way that the rod can be revolved about the z-axis at a constant angle a, as shown in Fig. 2. The rod is driven with constant angular velocity w about Oz. Use Lagrange method to derive the equation of motion for the bead. Use the distance of m from the origin as generalized coordinate and discuss the motion of the...
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