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Show that x(t) = x0 sin(ωt) is a solution of the undamped harmonic oscillator differential equation at small angles d^2x(t)/dt^2 = -ω 2x(t). For 7.5 points of extra credit, instead show that x(t) = x0e^-γt/2 cos(ωt) is a solution of the damped harmonic oscillator equation d^2x(t)/dt^2 = -ω 2x(t) - γ dx(t)/dt. You may assume γ^2<< 1.
Affect the local deformation and internal forces. What about the lateral transfer of a force on the same structure?
A uniform line charge of linear charge densitylambda=3.6nC/m extends fromx= 0 tox= 5 m What is the total charge?
A 5-kg fish swimming 1 m/s swallows an absent-minded 1-kg fish swimming toward it at a velocity that brings both fish to a halt immediately after lunch
An air puck of mass 0.29 kg is tied to a string and allowed to revolve in a circle of radius 1.4 m on a frictionless horizontal table. The other end of the string passes during a hole in the center of the table, and a mass of 0.7kg is tied to it. The..
One method for measuring the speed of sound uses standing waves. A cylindrical tube is open at both ends, and one end emits sound from a tuning fork. What is the speed of sound in the gas tube
A student applies a 20.-newton force to move a crate at a constant speed of 4.0 meters per second across a rough floor
A long solenoid consists of 1600 turns and has a length of 0.75 m. The current in the wire is 0.45 A. find the magnitude of the magnetic field inside the solenoid
Knowing that crank AB rotates counter clockwise at the constant rate of 300 rpm, determine the reaction at D when θ = 0.
A 2 kg block is dropped from 45 cm above a spring. If the spring compresses 5 cm when struck by the block, What is its spring constant
A golf ball traveling 3 m/s to the right has a head-on collision with a stationary bowling ball in a friction-free environment. If the collision is almost perfectly elastic, the speed of the golf ball immediately after the collision is:
Determine what is the absolute pressure at a depth of 10 meter in a lake, Determine what is the gauge pressure
How many electrons are transferred. What is the smallest thickness of a soap film that would appear black if illuminated with 490 light? imagine there is air on both sides of the soap film.
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