Q.11 - Excercises And ProblemsExpert-verified
An object in simple harmonic motion has amplitude and frequency , and at it passes through the equilibrium point moving to the right. Write the function that describes the object’s position.
function that describes the object's position is
The wave equation is in the form
The angular frequency is in the form
The initial condition is at , the object passes through the equilibrium to the right.
In order the cosine term to be zero it should satisfy the following condition:
The object is moving right in positive direction, so its velocity is positive at . The velocity function is the derivative of the position function:
Then, should be negative, therefore should be negative
The equation now takes the form of substituting the values of angular frequency
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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