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A. A point mass m moves frictionlessly on a horizontal plane. An...
9. (13 points) A block of mass m is attached to a top of a spring...
9. (13 points) A block of mass m is attached to a top of a spring (spring constant k). The bottom of the spring is attached to a car of mass M that is free to move on a horizontal track. The spring is rigid enough that it is only able to move up and down, not side to side. See below picture. m Hlllllll car a. Write the Lagrangian in terms of x, y, x, and y. b. Write...
A block of mass m is attached to a top of a spring (spring constant k)....
A block of mass m is attached to a top of a spring (spring constant k). The bottom of the spring is attached to a car of mass M that is free to move on a horizontal track. The spring is rigid enough that it is only able to move up and down, not side to side. See below picture. Illlllll car a. Write the Lagrangian in terms of x, y, i, and y. b. Write the Hamiltonian in terms...
Solve the following problems: Problem 1: masses&springs Two masses mand m2 connected by a spring of...
Solve the following problems:
Problem 1: masses&springs Two masses mand m2 connected by a spring of elastic constant k slide on a frictionless inclined plane under the effect of gravity. Let a be the angle between the the x axis and the inclined plane, r the distance between the two masses, l the position of the first mass with respect to the top of the plane (see figure). Considering the top of the plane to be the zero for potential...
I think I have most of this question set, but would appractite step by step explaination...
I think I have most of this
question set, but would appractite step by step explaination of
questions e), f), g), and h). Thanks!
Two masses m1and m2 connected by a spring of elastic constant k slide on a frictionless inclined plane under the effect of gravity. Let a be the angle between the the x axis and the inclined plane, r the distance between the two masses, l the position of the first mass with respect to the top...
3. A particle of mass m moves in one dimension, and has position r(t) at time t. The particle has...
Mechanics.
3. A particle of mass m moves in one dimension, and has position r(t) at time t. The particle has potential energy V(x) and its relativistic Lagrangian is given by where mo is the rest mass of the particle and c is the speed of light (a) Writing qr and denoting by p its associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy mzc2 6 marks (b) Write...
Consider a simple pendulum of length / and mass m placed in a rail-road cart that...
Consider a simple pendulum of length / and mass m placed in a rail-road cart that has constant acceleration a in the positive x-direction. (Hint: This means that suspension point of the pendulum moves with acceleration a, this needs to be accounted for when considering motion of the pendulum) a) (11 pts.) Find the Lagrangian function of this pendulum. b) (11 pts.) Obtain Lagrange's equations of motion for this pendulum. c) (11 pts.) Find the Hamiltonian function of this pendulum....
1. A particle of mass m moves in three dimensions, and has position r(t)-(x(t), y(t), z(t)) at ti...
Mechanics. Need help with c) and d)
1. A particle of mass m moves in three dimensions, and has position r(t)-(x(t), y(t), z(t)) at time t. The particle has potential energy V(x, y, 2) so that its Lagrangian is given by where i d/dt, dy/dt, dz/dt (a) Writing q(q2.93)-(r, y, z) and denoting by p (p,P2, ps) their associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy) H(q,p)H(g1, 92,9q3,...
Question 2 A pendulum is formed by suspending a mass m from the ceiling, using a...
Question 2 A pendulum is formed by suspending a mass m from the ceiling, using a spring of unstretched length lo and spring constant k (Figure 2). The pendulum moves in a fixed verticał plane. Choose x and y as the generalised coordinates. Set up the Lagrangian. Write down the equations of motion for the generalised variables. [4 marks] X Figure 2
A point mass with mass m slides on a smooth rod. The rod rotates with a...
A point mass with mass m slides on a smooth rod. The rod rotates
with a constant
around the origin on an x-y plane. Assume no external
forces.
a) Find Lagrangian of the point mass and the equation of
constraint.
b) Find Lagrange's equation of motion and eliminate the
constraint.
c) Write the Lagrange's equation with undetermined multipliers
and determine the constraint force.
We were unable to transcribe this imagem 0 = at X
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
9. (13 points) A block of mass m is attached to a top of a spring (spring constant k). The bottom of the spring is attached to a car of mass M that is free to move on a horizontal track. The spring is rigid enough that it is only able to move up and down, not side to side. See below picture. m Hlllllll car a. Write the Lagrangian in terms of x, y, x, and y. b. Write...
A block of mass m is attached to a top of a spring (spring constant k). The bottom of the spring is attached to a car of mass M that is free to move on a horizontal track. The spring is rigid enough that it is only able to move up and down, not side to side. See below picture. Illlllll car a. Write the Lagrangian in terms of x, y, i, and y. b. Write the Hamiltonian in terms...
Solve the following problems:
Problem 1: masses&springs Two masses mand m2 connected by a spring of elastic constant k slide on a frictionless inclined plane under the effect of gravity. Let a be the angle between the the x axis and the inclined plane, r the distance between the two masses, l the position of the first mass with respect to the top of the plane (see figure). Considering the top of the plane to be the zero for potential...
I think I have most of this
question set, but would appractite step by step explaination of
questions e), f), g), and h). Thanks!
Two masses m1and m2 connected by a spring of elastic constant k slide on a frictionless inclined plane under the effect of gravity. Let a be the angle between the the x axis and the inclined plane, r the distance between the two masses, l the position of the first mass with respect to the top...
Mechanics.
3. A particle of mass m moves in one dimension, and has position r(t) at time t. The particle has potential energy V(x) and its relativistic Lagrangian is given by where mo is the rest mass of the particle and c is the speed of light (a) Writing qr and denoting by p its associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy mzc2 6 marks (b) Write...
Consider a simple pendulum of length / and mass m placed in a rail-road cart that has constant acceleration a in the positive x-direction. (Hint: This means that suspension point of the pendulum moves with acceleration a, this needs to be accounted for when considering motion of the pendulum) a) (11 pts.) Find the Lagrangian function of this pendulum. b) (11 pts.) Obtain Lagrange's equations of motion for this pendulum. c) (11 pts.) Find the Hamiltonian function of this pendulum....
Mechanics. Need help with c) and d)
1. A particle of mass m moves in three dimensions, and has position r(t)-(x(t), y(t), z(t)) at time t. The particle has potential energy V(x, y, 2) so that its Lagrangian is given by where i d/dt, dy/dt, dz/dt (a) Writing q(q2.93)-(r, y, z) and denoting by p (p,P2, ps) their associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy) H(q,p)H(g1, 92,9q3,...
Question 2 A pendulum is formed by suspending a mass m from the ceiling, using a spring of unstretched length lo and spring constant k (Figure 2). The pendulum moves in a fixed verticał plane. Choose x and y as the generalised coordinates. Set up the Lagrangian. Write down the equations of motion for the generalised variables. [4 marks] X Figure 2
A point mass with mass m slides on a smooth rod. The rod rotates
with a constant
around the origin on an x-y plane. Assume no external
forces.
a) Find Lagrangian of the point mass and the equation of
constraint.
b) Find Lagrange's equation of motion and eliminate the
constraint.
c) Write the Lagrange's equation with undetermined multipliers
and determine the constraint force.
We were unable to transcribe this imagem 0 = at X
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
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