All AP Physics 1 Resources
Example Questions
Example Question #2 : Period And Frequency Of Harmonic Motion
Determine the period of a sine wave that has a frequency of .
Period is given by: where is frequency. Therefore,
Example Question #181 : Circular, Rotational, And Harmonic Motion
A horizontal spring with a constant is on a frictionless surface. If the mass is doubled, by what factor is the frequency of the spring changed? Assume simple harmonic motion.
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 attached to one end and is rotating in simple harmonic motion. If the frequency of the pendulum is , what is the length of the pendulum?
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 , by what factor does the period of the pendulum change when this is done?
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 #11 : Period And Frequency Of 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?
max U, max K
min U, min K
None of these
min U, max K
max U, min 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 #1091 : Newtonian Mechanics
Find the mass of the bob of a simple pendulum if the period of the pendulum is seconds, and the length 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 mass in an oscillating spring-mass system is given by the following equation:
, where is measured in , and is measured in .
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 , when the function is written as . Since frequency is the reciprocal of the period, we will need to flip the fraction.
Example Question #63 : Harmonic Motion
The position of a mass in an oscillating spring-mass system is given by the following equation:
, where is measured in , and is measured in .
What is the period of the oscillations?
In trigonometric functions, the period is always given by , when the function is written as . Once, we determine our value, we are halfway to the solution!
Example Question #64 : Harmonic Motion
A horizontal spring is oscillating with a mass sliding on a perfectly frictionless surface. If the amplitude of the oscillation is and the mass has a value of and a velocity at the rest length of , determine the frequency of oscillation.
None of these
Using conservation of energy:
Plugging in values:
Solving for
Plugging in values:
Example Question #1131 : Ap Physics 1
A wheel of radius rolls along a flat floor and makes rotations over a period of time. What distance has the wheel traveled?
In order to find the distance the wheel travels, we need a way to convert angular displacement to linear displacement. We know that the circumference of a circle (or a wheel, in this case) is . This means that in one rotation, the wheel would travel a distance equal to its circumference.
Distance of one rotation equals: .
Since the wheel travels rotations, the total distance that the wheel travels will be equal to the distance traveled by one rotation multiplied by the number of rotations.
Distance of rotations equals:
Certified Tutor