Astronauts in space cannot weigh themselves by standing on a bathroom scale. Instead, they determine their mass by oscillating on a large spring. Suppose an astronaut attaches one end of a large spring to her belt and the other end to a hook on the wall of the space capsule. A fellow astronaut then pulls her away from the wall and releases her. The spring's length as a function of time is shown in FIGURE.
a. What is her mass if the spring constant is
b. What is her speed when the spring's length is
a. The mass spring constant is .
b. The speed is .
In simple harmonic motion, the period of an oscillator is given by
Maximum displacement is,
Speed has magnitude velocity of ,
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?
It is said that Galileo discovered a basic principle of the pendulum—
that the period is independent of the amplitude—by 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 ?
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