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A pendulum of length l and mass m hangs from a bead of mass M that moves frictionlessly along the curve y=x^4 . Use y, the height of the bead above its lowest point, and θ, the angle of the pendulum with respect to the vertical, as the generalized coordinates,
(a) Find the Lagrangian of the system.
(b) Find the Lagrange's equations of motion.
(c) Simplify the equations of motion in case both coordinates are very small.
The index of refraction for red light in water is 1.331 and that for blue light is 1.340. What is the underwater angle of refraction for the blue component of the light
Compare the difference between the insolation on the north and south faces in each session with the seasonal variation on each face. Ignore eccentricity and atmospheric absorption.
A laser beam is projected through a diffraction grating which has a slit to slit separation of 2 microm (5000 lines/cm). What is the wavelength of the laser
a spring has a spring constant of 400 N/m. the spring is compressed 15 cm and a 2 kg ball is placed on the spring in its compressed state. what is the potential energy of the spring in its compressed state
The pressure inside a gas bottle at 23.4 °C is 4350 kPa. What will be the pressure inside the bottle
A bullet is fired horizontally with an initial velocity of 900m/s at a target located 150 m/s which takes .167 seconds to reach. Using the approx value of g=10 m/s2, how far does the bullet fall in this time.
A 1.0 kg rod rests on two horizontal rails 1.0 m apart and carries a current of 50 A from one rail to the other. The coefficient of static friction between rod and rails is 0.60. What are the magnitude and angle (relative to the vertical) of the smal..
The intensity of sunlight at the Earth's surface on a fairly clear day is 1000W/m2. [20pts], What is the maximum value of the electric field
A cargo plane is flying horizontally at an altitude of 20.0 km with a speed of 888 km/h when a large crate falls out of the rear loading ramp. How far is the crate from the aircraft when the crate hits the ground
A 3.5-cm tall object is viewed through a converging lens. When the lens moves from one place to another, the orientation of the image changes from upright to inverted. How far from the object does the lens stop
During a violent storm, a car is struck by a failing high-voltage wire that puts an excess charge of -850 mircoC on the metal car. how much is on the outer surface of the car
The displacement of a wave traveling in the negative x-direction is y(t)=( 5.6cm )cos( 5.2 x + 73 t), find the wavelength, frequency, and speed of this wave
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