AP Physics 1 : Circular, Rotational, and Harmonic Motion
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Example Questions
Example Question #181 : Circular, Rotational, And Harmonic Motion
If a period of a pendulum is 
None of these
Equation for period of a pendulum:
Solve.
Example Question #4 : Period And Frequency Of Harmonic Motion
In the lab, a student has created an oscillator by hanging a weight from a spring. The student releases the oscillator from rest and uses a sensor and computer to find the equation of motion for the oscillator:
The student then replaces the weight with a weight whose mass, 
The equation of motion for an oscillator is:
In words, the position as a function of time equals the amplitude times the cosine of the sum of the frequency (in radians per second) times time plus phase. Changing the mass of the weight only changes the frequency, but it depends upon the square root of the mass. Since increasing the mass increases the period, it decreases the frequency by the factor of 
Example Question #2 : Period And Frequency Of Harmonic Motion
The Fourier Transform is an extensively used mathematical analysis technique. In some applications, it reconstructs a function 
Given that the Fourier Transform is given by the series:
Where 
First, we want to ignore the summation sign and the 
For 
Remember that wavelength 
Example Question #182 : Circular, Rotational, And Harmonic Motion
Determine the period of a sine wave that has a frequency of 
Period is given by: 
Example Question #181 : Circular, Rotational, And Harmonic Motion
A horizontal spring with a constant 
The expression for the frequency of a spring:
Therefore, we can say:
Where:
Substituting this into our expression, we get:
Taking the inverse of both sides:
Rearranging for final frequency:
From the problem statement, we know that:
substituting this into the expression, we get:
Therefore, the frequency was changed by a factor of
Example Question #182 : Circular, Rotational, And Harmonic Motion
A simple pendulum has a block of mass 
We only need one expression to solve this problem:
Now we just need to rearrange for the length of the pendulum:
We have values for each of these variables, so time to plug and chug:
Example Question #11 : Period And Frequency Of Harmonic Motion
If the length of a simple pendulum is halved and the pendulum is moved to the moon where 
Since we are told that this is a simple pendulum, we can use the follow expression for period:
Now let's divide scenario 2 by scenario 1:
From the problem statement, we know that:
So let's plug that in:
Then plugging in our values for g:
Example Question #183 : Circular, Rotational, And Harmonic Motion
As on object passes through its equilibrium position during simple harmonic motion, which statements are true regarding its potential (U) and kinetic (K) energies?
min U, max K
min U, min K
max U, min K
None of these
max U, max K
min U, max K
An object has the maximum potential energy the furthest from its equilibrium point (at the turnaround point). So it at the equilibrium position it would have the minimum potential energy. If it is undergoing simple harmonic motion, it would have the maximum kinetic energy as it passes through the equilibrium position because it is returning from the stretched position (spring example) where it gathered energy. The same is true for other objects undergoing this motion.
Example Question #184 : Circular, Rotational, And Harmonic Motion
Find the mass of the bob of a simple pendulum if the period of the pendulum is 
Impossible to determine
Impossible to determine
It's impossible because the period of a simple pendulum doesn't depend on the mass of the bob. Because of this, we have no way to determine the mass from the period.
Example Question #185 : Circular, Rotational, And Harmonic Motion
The position of a 
What is the frequency of the system?
In these types of problems, it is always advantageous to recognize the format of the equation. In trigonometric functions, the period is always given by 
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