An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at . It then oscillates with a period of and a maximum speed of .
a. What is the amplitude of the oscillation?
b. What is the glider’s position at ?
a. The oscillation has an amplitude of .
b. The glider’s position at is .
Time period, .
Maximum speed, .
Where, is the angular frequency.
Substitute the values of and to obtain .
The oscillation has an amplitude of
Initial condition, ,.
Equation of the simple harmonic motion is .
Where, is the amplitude, is the position, is the angular frequency and is the phase.
At time , the position of the glider is .
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?
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