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Chapter 15: Q.6 (page 414)
A block oscillating on a spring has an amplitude of . What will the amplitude be if the total energy is doubled? Explain.
The new amplitude of the block when the total energy is doubled after rounding off to three significant figures is .
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A oscillator has a speed of when its displacement is role="math" localid="1651383318687" and when its displacement is . What is the oscillator鈥檚 maximum speed?
A 0.300 kg oscillator has a speed of 95.4 cm/s when its displacement is 3.00 cm and 71.4 cm/s when its displacement is 6.00 cm. What is the oscillator鈥檚 maximum speed?
It is said that Galileo discovered a basic principle of the pendulum鈥�
that the period is independent of the amplitude鈥攂y using
his pulse to time the period of swinging lamps in the cathedral
as they swayed in the breeze. Suppose that one oscillation of a
swinging lamp takes.
a. How long is the lamp chain?
b. What maximum speed does the lamp have if its maximum
angle from vertical is ?
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?
What are the (a) amplitude, (b) frequency, and (c) phase constant of the oscillation shown in
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