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 ?
(a) The phase constant is
(b) The phase at is , at is , at is , at is
left of equilibrium position
to the right side of the equilibrium position
Equation of wave is given,
We have to search out the Amplitude by divide the above equations,
Substitute the values and at ,
The absolute angle is , and also the displacement is , thus the direction is from to at , where , that the angle is within the third quadratic and is given from by,
Then, , we write within the variety of
To achieve the best possible positive amplitude,
so, the equation is
The angle is,
A captive James Bond is strapped to a table beneath a huge
pendulum made of a -diameter uniform circular metal blade
rigidly attached, at its top edge, to a -long, massless rod.
The pendulum is set swinging with a amplitude when its lower
edge is above the prisoner, then the table slowly starts ascending
at . After minutes, the pendulum’s amplitude
has decreased to . Fortunately, the prisoner is freed with a
mere to spare. What was the speed of the lower edge of the
blade as it passed over him for the last time?
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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