Period of SHM - Physics
Card 0 of 40
A mass is placed at the end of a spring. It has a starting velocity of 
and is allowed to oscillate freely. If the mass has a starting velocity of 
, what would the period be?
A mass is placed at the end of a spring. It has a starting velocity of 
When it comes to the period of a spring, the velocity of the object has no effect.
The equation is 
When it comes to the period of a spring, the velocity of the object has no effect.
The equation is
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A spring is attached to a mass, oscillating freely in simple harmonic motion. What change can be made to increase the period of the oscillation?
A spring is attached to a mass, oscillating freely in simple harmonic motion. What change can be made to increase the period of the oscillation?
The equation for the period of a spring in simple harmonic motion is:
In this formula, m is the mass and k is the spring constant. The only two things we can adjust that can change the period, then, are the mass and spring constant. The length of the spring and the acceleration due to gravity are irrelevant.
If we increase the mass we get a larger numerator, which in turns will give us a larger period. If we decrease the mass we get a smaller numerator, which would give us a smaller period. If we use a higher spring constant we get a larger denominator, which also gives us a smaller period.
The equation for the period of a spring in simple harmonic motion is:
In this formula, m is the mass and k is the spring constant. The only two things we can adjust that can change the period, then, are the mass and spring constant. The length of the spring and the acceleration due to gravity are irrelevant.
If we increase the mass we get a larger numerator, which in turns will give us a larger period. If we decrease the mass we get a smaller numerator, which would give us a smaller period. If we use a higher spring constant we get a larger denominator, which also gives us a smaller period.
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Your grandfather clock’s pendulum has a length of 
. If the clock loses half a minute per day, how should you adjust the length of the pendulum?
Your grandfather clock’s pendulum has a length of 
We also can calculate the total number of seconds in a day.
There are 
seconds in one day.
Therefore we want our clock to swing a certain number of times with a period of 
to equal 
.
We know that our current clock has a certain number of swings with a period of 
to equal 
So we have
We can calculate the current period of the pendulum using the equation
We can set up a ratio of each of these two periods to determine the missing length.
Notice that 2, pi and g are all in both the numerator and denominator and therefore fall out of the problem.
We can now solve for our missing piece.
Square both sides to get rid of the square root.
We should lengthen the pendulum by 
We also can calculate the total number of seconds in a day.
There are 
Therefore we want our clock to swing a certain number of times with a period of 
We know that our current clock has a certain number of swings with a period of 
So we have
We can calculate the current period of the pendulum using the equation
We can set up a ratio of each of these two periods to determine the missing length.
Notice that 2, pi and g are all in both the numerator and denominator and therefore fall out of the problem.
We can now solve for our missing piece.
Square both sides to get rid of the square root.
We should lengthen the pendulum by
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A spring has a 
mass attached to one, which oscillates with a period of 
. What is the frequency?
A spring has a 
The mass has no bearing on the relationship between frequency and period. This relationship is given by the equation:
Given the period, the frequency will be equal to its reciprocal.
The mass has no bearing on the relationship between frequency and period. This relationship is given by the equation:
Given the period, the frequency will be equal to its reciprocal.
Compare your answer with the correct one above
A spring has a spring constant of 
. If a force of 
is used to stretch out the spring, what is the total displacement of the spring?
A spring has a spring constant of 
For this problem, use Hooke's law:
In this formula, 
is the spring constant, 
is the compression of the spring, and 
is the necessary force. We are given the spring constant and the force, allowing us to solve for the displacement.
Plug in our given values and solve.
Note that both the force and the displacement are positive because the stretching force will pull in the positive direction. If the spring were compressed, the change in distance would have been negative.
For this problem, use Hooke's law:
In this formula, 
Plug in our given values and solve.
Note that both the force and the displacement are positive because the stretching force will pull in the positive direction. If the spring were compressed, the change in distance would have been negative.
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A man swings a bucket back and forth at the end of a rope, creating a pendulum. What factor could be used to increase the period of the pendulum?
A man swings a bucket back and forth at the end of a rope, creating a pendulum. What factor could be used to increase the period of the pendulum?
The equation for the period of a pendulum is:
Notice that the material of the pendulum and the mass at the end do not enter into the equation at all. The only things that are capable of affecting the period are the length of the pendulum and the acceleration due to gravity.
While changing the altitude of the pendulum will change the period, it will do it only slightly unless you take it miles above the earth's crust. Furthermore, decreasing the altitude of the pendulum will increase the force due to gravity, which will result in a decreased period. The best answer is to increase the length of the rope. This will increase the period of the pendulum.
The equation for the period of a pendulum is:
Notice that the material of the pendulum and the mass at the end do not enter into the equation at all. The only things that are capable of affecting the period are the length of the pendulum and the acceleration due to gravity.
While changing the altitude of the pendulum will change the period, it will do it only slightly unless you take it miles above the earth's crust. Furthermore, decreasing the altitude of the pendulum will increase the force due to gravity, which will result in a decreased period. The best answer is to increase the length of the rope. This will increase the period of the pendulum.
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What is the period of a simple pendulum 
long when it is in a freely falling elevator?
What is the period of a simple pendulum 
The period of a simple pendulum on the free-falling is infinite because at a time of free-falling elevator the gravitational constant will equal zero which leads to an increase in the value in the numerator to infinite. Thus, the period of time in a free-falling elevator is infinite.
The period of a simple pendulum on the free-falling is infinite because at a time of free-falling elevator the gravitational constant will equal zero which leads to an increase in the value in the numerator to infinite. Thus, the period of time in a free-falling elevator is infinite.
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If a particle undergoes Simple Harmonic motion with an amplitude of 
. What is the total distance it travels in one period?
If a particle undergoes Simple Harmonic motion with an amplitude of 
The period is how long it takes to complete one oscillation. In this case, a complete oscillation would take the object 
away from the center (the amplitude), travel back to the center, travel below the equilibrium point 
away, and then travel back to the center. Therefore the total distance traveled is 
times the amplitude as it must travel away, back, below, and back again. Therefore the total distance traveled is 
.
The period is how long it takes to complete one oscillation. In this case, a complete oscillation would take the object 
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How long must a simple pendulum be if it is to make exactly one swing per second? (That is one complete oscillation would take 2 seconds.)
How long must a simple pendulum be if it is to make exactly one swing per second? (That is one complete oscillation would take 2 seconds.)
The equation to determine the period of pendulum is
We can rearrange this equation to solve for length (
).
We can now solve for the length knowing that the period of the pendulum is 2 seconds.
The equation to determine the period of pendulum is
We can rearrange this equation to solve for length (
We can now solve for the length knowing that the period of the pendulum is 2 seconds.
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A pendulum has a period of 
on Earth. What is its period on Mars, where the acceleration due to gravity is about 
that on Earth?
A pendulum has a period of 
To begin we want to determine the original length of the pendulum.
The equation to determine the period of pendulum is
We can rearrange this equation to solve for length (
).
We can now solve for the length knowing that the period of the pendulum is 2 seconds.
Now we can use the same equation and instead substitute in the value for the acceleration due to gravity on Mars.
To begin we want to determine the original length of the pendulum.
The equation to determine the period of pendulum is
We can rearrange this equation to solve for length (
We can now solve for the length knowing that the period of the pendulum is 2 seconds.
Now we can use the same equation and instead substitute in the value for the acceleration due to gravity on Mars.
Compare your answer with the correct one above
A mass is placed at the end of a spring. It has a starting velocity of and is allowed to oscillate freely. If the mass has a starting velocity of , what would the period be?
A mass is placed at the end of a spring. It has a starting velocity of
When it comes to the period of a spring, the velocity of the object has no effect.
The equation is
When it comes to the period of a spring, the velocity of the object has no effect.
The equation is
Compare your answer with the correct one above
A spring is attached to a mass, oscillating freely in simple harmonic motion. What change can be made to increase the period of the oscillation?
A spring is attached to a mass, oscillating freely in simple harmonic motion. What change can be made to increase the period of the oscillation?
The equation for the period of a spring in simple harmonic motion is:
In this formula, m is the mass and k is the spring constant. The only two things we can adjust that can change the period, then, are the mass and spring constant. The length of the spring and the acceleration due to gravity are irrelevant.
If we increase the mass we get a larger numerator, which in turns will give us a larger period. If we decrease the mass we get a smaller numerator, which would give us a smaller period. If we use a higher spring constant we get a larger denominator, which also gives us a smaller period.
The equation for the period of a spring in simple harmonic motion is:
In this formula, m is the mass and k is the spring constant. The only two things we can adjust that can change the period, then, are the mass and spring constant. The length of the spring and the acceleration due to gravity are irrelevant.
If we increase the mass we get a larger numerator, which in turns will give us a larger period. If we decrease the mass we get a smaller numerator, which would give us a smaller period. If we use a higher spring constant we get a larger denominator, which also gives us a smaller period.
Compare your answer with the correct one above
Your grandfather clock’s pendulum has a length of . If the clock loses half a minute per day, how should you adjust the length of the pendulum?
Your grandfather clock’s pendulum has a length of
We also can calculate the total number of seconds in a day.
There are seconds in one day.
Therefore we want our clock to swing a certain number of times with a period of to equal .
We know that our current clock has a certain number of swings with a period of to equal
So we have
We can calculate the current period of the pendulum using the equation
We can set up a ratio of each of these two periods to determine the missing length.
Notice that 2, pi and g are all in both the numerator and denominator and therefore fall out of the problem.
We can now solve for our missing piece.
Square both sides to get rid of the square root.
We should lengthen the pendulum by
We also can calculate the total number of seconds in a day.
There are
Therefore we want our clock to swing a certain number of times with a period of
We know that our current clock has a certain number of swings with a period of
So we have
We can calculate the current period of the pendulum using the equation
We can set up a ratio of each of these two periods to determine the missing length.
Notice that 2, pi and g are all in both the numerator and denominator and therefore fall out of the problem.
We can now solve for our missing piece.
Square both sides to get rid of the square root.
We should lengthen the pendulum by
Compare your answer with the correct one above
A spring has a mass attached to one, which oscillates with a period of . What is the frequency?
A spring has a
The mass has no bearing on the relationship between frequency and period. This relationship is given by the equation:
Given the period, the frequency will be equal to its reciprocal.
The mass has no bearing on the relationship between frequency and period. This relationship is given by the equation:
Given the period, the frequency will be equal to its reciprocal.
Compare your answer with the correct one above
A spring has a spring constant of . If a force of is used to stretch out the spring, what is the total displacement of the spring?
A spring has a spring constant of
For this problem, use Hooke's law:
In this formula, is the spring constant, is the compression of the spring, and is the necessary force. We are given the spring constant and the force, allowing us to solve for the displacement.
Plug in our given values and solve.
Note that both the force and the displacement are positive because the stretching force will pull in the positive direction. If the spring were compressed, the change in distance would have been negative.
For this problem, use Hooke's law:
In this formula,
Plug in our given values and solve.
Note that both the force and the displacement are positive because the stretching force will pull in the positive direction. If the spring were compressed, the change in distance would have been negative.
Compare your answer with the correct one above
A man swings a bucket back and forth at the end of a rope, creating a pendulum. What factor could be used to increase the period of the pendulum?
A man swings a bucket back and forth at the end of a rope, creating a pendulum. What factor could be used to increase the period of the pendulum?
The equation for the period of a pendulum is:
Notice that the material of the pendulum and the mass at the end do not enter into the equation at all. The only things that are capable of affecting the period are the length of the pendulum and the acceleration due to gravity.
While changing the altitude of the pendulum will change the period, it will do it only slightly unless you take it miles above the earth's crust. Furthermore, decreasing the altitude of the pendulum will increase the force due to gravity, which will result in a decreased period. The best answer is to increase the length of the rope. This will increase the period of the pendulum.
The equation for the period of a pendulum is:
Notice that the material of the pendulum and the mass at the end do not enter into the equation at all. The only things that are capable of affecting the period are the length of the pendulum and the acceleration due to gravity.
While changing the altitude of the pendulum will change the period, it will do it only slightly unless you take it miles above the earth's crust. Furthermore, decreasing the altitude of the pendulum will increase the force due to gravity, which will result in a decreased period. The best answer is to increase the length of the rope. This will increase the period of the pendulum.
Compare your answer with the correct one above
What is the period of a simple pendulum long when it is in a freely falling elevator?
What is the period of a simple pendulum
The period of a simple pendulum on the free-falling is infinite because at a time of free-falling elevator the gravitational constant will equal zero which leads to an increase in the value in the numerator to infinite. Thus, the period of time in a free-falling elevator is infinite.
The period of a simple pendulum on the free-falling is infinite because at a time of free-falling elevator the gravitational constant will equal zero which leads to an increase in the value in the numerator to infinite. Thus, the period of time in a free-falling elevator is infinite.
Compare your answer with the correct one above
If a particle undergoes Simple Harmonic motion with an amplitude of . What is the total distance it travels in one period?
If a particle undergoes Simple Harmonic motion with an amplitude of
The period is how long it takes to complete one oscillation. In this case, a complete oscillation would take the object away from the center (the amplitude), travel back to the center, travel below the equilibrium point away, and then travel back to the center. Therefore the total distance traveled is times the amplitude as it must travel away, back, below, and back again. Therefore the total distance traveled is .
The period is how long it takes to complete one oscillation. In this case, a complete oscillation would take the object
Compare your answer with the correct one above
How long must a simple pendulum be if it is to make exactly one swing per second? (That is one complete oscillation would take 2 seconds.)
How long must a simple pendulum be if it is to make exactly one swing per second? (That is one complete oscillation would take 2 seconds.)
The equation to determine the period of pendulum is
We can rearrange this equation to solve for length ().
We can now solve for the length knowing that the period of the pendulum is 2 seconds.
The equation to determine the period of pendulum is
We can rearrange this equation to solve for length (
We can now solve for the length knowing that the period of the pendulum is 2 seconds.
Compare your answer with the correct one above
A pendulum has a period of on Earth. What is its period on Mars, where the acceleration due to gravity is about that on Earth?
A pendulum has a period of
To begin we want to determine the original length of the pendulum.
The equation to determine the period of pendulum is
We can rearrange this equation to solve for length ().
We can now solve for the length knowing that the period of the pendulum is 2 seconds.
Now we can use the same equation and instead substitute in the value for the acceleration due to gravity on Mars.
To begin we want to determine the original length of the pendulum.
The equation to determine the period of pendulum is
We can rearrange this equation to solve for length (
We can now solve for the length knowing that the period of the pendulum is 2 seconds.
Now we can use the same equation and instead substitute in the value for the acceleration due to gravity on Mars.
Compare your answer with the correct one above