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Chapter 15: Q. 33 (page 416)
The amplitude of an oscillator decreases to 36.8% of its initial value in 10.0 s. What is the value of the time constant?
The Time Constant is 5.0
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A g ball is tied to a string. It is pulled to an angle of and released to swing as a pendulum. A student with a stopwatch finds that oscillations take. How long is the string?
FIGURE P15.62 is a top view of an object of mass connected between two stretched rubber bands of length . The object rests on a frictionless surface. At equilibrium, the tension in each rubber band is . Find an expression for the frequency of oscillations perpendicular to the rubber bands. Assume the amplitude is sufficiently small that the magnitude of the tension in the rubber bands is essentially unchanged as the mass oscillates.
For a particle in simple harmonic motion, show that where is the average speed during one cycle of the motion.
An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk driven back and forth in at by an electromagnetic coil.
a. The maximum restoring force that can be applied to the disk without breaking it is . What is the maximum oscillation amplitude that won't rupture the disk?
b. What is the disk's maximum speed at this amplitude?
An air-track glider attached to a spring oscillates with a period of . At the glider is left of the equilibrium position and moving to the right at .
a. What is the phase constant?
b. What is the phase at , , , and ?
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