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Consider a linear model of a molecule with three atoms. The outer atoms are of mass m and the atom in the molecules center is of mass M. The outer atoms are connected to the center atom through springs of a constant k.
(a) Determine the Lagrange function of the system. Use as coordinates the deviations of the atoms from their equilibrium position.
(b) Determine the Eigen frequencies of the system and corresponding eigenvectors.
(c) Write down the general solution of the equation of motion of the system.
The puck in figure has a mass of .135 kg. If its original distance from the center of rotation is 31.2 cm, Determine the work put on the puck
A 4.9 m diameter merry-go-round is rotating freely with an angular velocity of 0.780 rad/s. Its total moment of inertia is 1550kg*m2. Four people standing on the ground, each of mass63.6 kg, abruptly step onto the edge of the merry-go-round.
Steams flows through an adiabatic turbine with a mass flow rate of 4.5 kg/sec, 500 degrees Celsius and 6 MPa. Calculate power output from the adiabatic turbine
explain the energy released in the explosion. A rock stuck in the tread of a 59.0 cm diameter bicycle wheel has a tangential speed of 3.20 m/s. When the brakes are applied, the rock's tangential deceleration is 1.20 m/s^2
Light from an argon laser strikes a diffraction grating that has 5306 lines per centimeter. Determine the wavelength of the laser light
A peregrine falcon dives at a pigeon. The falcon starts with zero downward velocity and dives with the free-fall acceleration. how long does it take the falcon to intercept the pigeon
Six pendulums of mass and length are released from rest at the similar angle from vertical. Rank the pendulums according to the number of complete cycles of motion each pendulum goes through per minute.
A rocket is fired at a speed of 75.0 m/s from ground level, at an angle of 56.5° above the horizontal. By how much does the rocket clear the top of the wall
A toy airplane is tied to the ceiling with a string. When the airplane's motor is started, it moves with a constant speed of 1.03m/s in a horizontal circle. If the angle the string makes with the vertical is 27°, and the tension of the string is 1N.
An 8.30 kg stone at rest on a spring. The spring is compressed 11 cm by the stone. The stone is after that pushed down an additional 26.00 cm and free. To what highest height (in cm) does the stone rise from that position.
A transformer has 3,840 turns in the secondary. The inputvoltage is 110V, the output current is 6.5A. the input current is0.5A. Calculate the output voltage
A map suggests that Atlanta is 730 miles in a direction 5.00° north of east from Dallas. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago
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