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Chapter 15: Q. 47 (page 417)
A block hangs in equilibrium from a vertical spring. When a second identical block is added, the original block sags by . What is the oscillation frequency of the two-block system?
The two block system have oscillation frequency of.
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Scientists are measuring the properties of a newly discovered elastic material. They create a -m-long, -mm-diameter cord, attach an mass to the lower end, then pull the mass down and release it. Their high-speed video camera records oscillations in . What is Young's modulus of the material?
A solid sphere of mass and radius is suspended from a thin rod, as shown in
The sphere can swing back and forth at the bottom of the rod. Find an expression for the frequency of small angle oscillations.
A spring with spring constant hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down and released. If the ball makes oscillations in localid="1650030754517" , what are its localid="1650030759248" mass and localid="1650030763230" maximum speed?
Suppose a large spherical object, such as a planet, with radius and mass has a narrow tunnel passing diametrically through it. A particle of mass m is inside the tunnel at a distance from the center. It can be shown that the net gravitational force on the particle is due entirely to the sphere of mass with radius ; there is no net gravitational force from the mass in the spherical shell with .
. Find an expression for the gravitational force on the particle, assuming the object has uniform density. Your expression will be in terms of , , , , and any necessary constants.
. You should have found that the gravitational force is a linear restoring force. Consequently, in the absence of air resistance, objects in the tunnel will oscillate with . Suppose an intrepid astronaut exploring a -km-diameter, kg asteroid discovers a tunnel through the center. If she jumps into the hole, how long will it take her to fall all the way through the asteroid and emerge on the other side?
An object in simple harmonic motion has amplitude and frequency , and at it passes through the equilibrium point moving to the right. Write the function that describes the object’s position
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