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Three identical masses m are connected to 2 identical springs of stiffness k and equilibrium length b, as shown in the figure above. The masses are free to oscillate in one dimension along an axis that runs through all three. They lie on a level, frictionless, horizontal surface. Introduce coordinates, x1, x2 and x3 to measure their displacement from some fixed point on this axis.
Express the Lagrangian of the system in terms of these coordinates and their velocities. Then introduce the coordinates n1, n2, and n3, that measure the displacements of the springs from their equilibrium positions. Write the Lagrangian in terms of these coordinates and their time derivatives. Then find the kinetic and potential energy matrices. What are the frequencies of vibration for the normal modes of this system? What are eigenvectors?
In a nuclear experiment a proton with kinetic energy 3.5 MeV moves in a circular path in a uniform magnetic field. a)If the magnetic field is B = 1.1 T what is the radius of the orbit? b) What energy must an alpha particle (q = +2e, m = 4.0 u) and a ..
The springs of a 1500kg car compress 6.0mmwhen its 61kg driver gets into the driver's seat. what will be the frequency of oscillations
The primary coil of a step-up transformer is connected across the terminals of a standard wall socket, and resistor 1 with aresistance R1 is connected across the secondary coil. The currentin the resistor is then measured.
Find the intensity of the starlight at the Earth, Find the power of the starlight the Earth intercepts. One light-year is the distance traveled by the light through a vacuum in one year
A loudspeaker of mass 25 is suspended a distance of = 1.60 below the ceiling by two cables that make equal angles with the ceiling. Each cable has the length of = 3.30.
bob whose mass is 36 kg stands at the center of a 200 kg merry-go-round that is spinning at 30 rpm. What is the spinning rate now
The air pressure above the liquid in figure is 0.532 atm. Determine the air pressure in the bubble suspended in the liquid
a box is sliding up an incline plane that has an angle of 15degrees with the horizontal. how far does the box travel up the plane
A uniform, solid metal disk of mass 6.50kg and diameter 24.0 cmhangs in a horizontal plane, supported at its center by a verticalmetal wire. You find that it requires a horizontal force of 4.23 Ntangent to the rim of the disk to turn it by 3.34 degre..
A parallel plate capacitor by plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.)
A chair of weight 125 N lies atop a horizontal floor; the floor is not frictionless. You push on the chair with a force of F = 35.0 N directed at an angle of 42.0 below the horizontal and the chair slides along the floor. Using Newton's laws, compute..
Calculate Earth's average speed relative to the Sun (in m/s). According to my book, the answer is 3.0x10^4 m/s
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