- Good morning.
A horizontal mass spring system is where a mass is attached to a spring oriented horizontally,
and then placed on a frictionless surface.
Flipping Physics
Who are the three of you?
- We are your substitute students. My name is Olivia.
- I'm Kevin.
- Hey, I’m Anish.
- Sure. Hello there Olivia, Kevin, Anish.
Substitute students! Yeah, that makes sense.
Okay, here we go.
When the mass is at rest, the spring will be at the equilibrium or rest position.
Let’s add a dotted line there to indicate this is the equilibrium position.
Now let's pull the mass to the right and hold it there.
We can call this position one.
Anish, when the mass is at position one, what is the direction of the spring force acting on the mass?
- At position number one, x, the displacement from equilibrium position, is to the right, therefore,
according to Hooke’s Law, the spring force acting on the mass will be in the opposite direction, or to the left.
- Correct.
Now we can let go of the mass and watch as the mass is accelerated to the left by the force of the spring.
Notice the mass passes through rest position and will go all the way over to the left,
and let's pause it there for a moment.
Let's call position two the location of the mass when it is at equilibrium position,
and position three the location of the mass when it is at its maximum displacement from equilibrium position
to the left.
- Olivia, what is the direction of the spring force on the mass when the mass is at position two?
- That question does not make any sense
because the displacement from equilibrium position at number two is zero.
Therefore, according to Hooke's law, the force of the spring is also zero and has no direction.
- That is correct, Olivia. Thank you.
- Kevin, what about the direction of the force of the spring when it is at position three?
- At position number three the
displacement of the mass from the rest position is to the left;
therefore, the force of the spring is from the right.
- That is also correct. Thank you Kevin.
- let's go back to the beginning of this demonstration for a moment and watch what happens.
The mass is released at position one, then it slides through position two
pauses at position three before going back the other direction and notice what happens.
The mass will continue to oscillate back and forth going through these positions in this order,
1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2,
1, 2, 3, 2, 1, 2, 3...
and Kevin, in the absence of friction, when will the pattern of this mass spring system end?
- If there is no friction, it will never end.
- Correct. This is called simple harmonic motion.
This mass spring system is in simple harmonic motion.
It will continue to oscillate back and forth like this forever in the absence of friction.
There are two requirements for the force that causes simple harmonic motion.
First, the force causing simple harmonic motion must be a restoring force.
Remind me Anish, what is a restoring force?
- A restoring force is a force that's always directed towards the rest position.
- Correct. Notice this means the restoring force will always accelerate the mass toward equilibrium position.
Second, the magnitude of the restoring force
must also be proportional to the displacement from equilibrium position.
Olivia, how do we know the magnitude of the spring force is proportional to x,
the displacement from rest position?
- According to Hooke's law, the force of the spring equals the negative of k, the spring constant, times
x, the displacement from equilibrium position,
therefore as x increases, the magnitude of the spring force will also increase.
Therefore, the magnitude of the force of the spring is proportional to the displacement from rest position.
- Absolutely.
Thank you very much for learning with me today.
I enjoyed learning with you.