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Consider a particle of mass m moving in a vertical x-y plane along a curve y=acos(2xπ/λ). free fall acceleration is g. First consider two coordinates x and y:a) write down lagrangian of systemb) obtain lagrange's equation of motion with undetermined multipliers.c) define the forces of the constraint. what is the minimal velocity of a particle at the top of a curve when the force of constrain vanishes? compare your expressions for the forces of constraint with the forces you would introduce to formulate the problem in terms of newtons second law.Now choose a single generalized coordinate corresponding to a horizontal coordinate x.d) write down the lagrangian of the particle and lagrange's equations of motion.e) Define the generalized momentum and write down the hamiltonian of the particle.f) derive the canonical(Hamilton's) equation of motion.g) demonstrate that the canonical equations of motions can be reduced to lagrange's equation of motion.
Adjacent antinodes of a standing wave on a string are 15.0 cm apart. Find the maximum and minimum transverse speeds of a point at an antinode
However, as the drawing shows, a plane mirror reflects light from the bird into your camera. If x = 4.2 m and y = 3.9 m in the drawing, for what distance must you set focus of the camera lens in order to snap a sharp picture of the bird's image.
Two forces act on a block of wood. The first force has a magnitude of 8.66 N in a direction 12.0 degrees counterclockwise from the positive x-axis, What is the magnitude of the resulting force
Hyperthermia is one of the modalities for cancer treatment. In the procedure, the magnetic nanoparticles are injected at the tumor site which is then exposed to radio frequency electromagnetic waves. what is the inductance of the solenoid
An object is subject to a restoring force F = 8x3, How much work must be done to move the object from x = 0.10 to x = 0.47 m
A crate of 30.2- tools rests on a horizontal floor. You exert a regularly increasing horizontal push on it and observe that the crate just begins to move while your force exceeds 319. After that you must reduce your push to 227 to keep it moving at a..
A magnetic field of 3 Tesla is oriented into the page. A 10 cm long conducting bar is pulled to the right at a constant speed of 3.4 m/s. What is the magnitude of the current in the bar
Two particles, with charges of q1 = 60.0nC and q2 = 60.0nC, are placed at the points with coordinates (0, 12.00 cm) and (0, 12.00 cm). A particle with charge q3 = 30.0 nC is located at the origin.(a) Find the electric potential energy of the confi..
The position of a 50 g oscillating mass is given by x(t) = (2.0 cm) cos(5t), where t is in seconds. Determine the following. (a) The amplitude. (b) The period. (c) The spring constant. (d) The maximum speed
A circular loop of diameter 10 cm, carrying a current of 0.20 A, is placed inside a magnetic field = 0.30 T. Calculate the magnitude of the torque on the loop due to the magnetic field
Two parallel plates having charges of equal magnitude but opposite sign are separated by 24.0 cm. Determine the force on the proton
Sketch a principle ray diagram showing the formation of the image. compute the position, size, orientation (erect or inverted), and nature (real or virtual) of the image.
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