How do I calculate kinetic energy in oscillation problems?

[Cici2017]

Homework Statement

Homework Equations

The Attempt at a Solution

What do I do next to work out kinetic energy?

 

[Orodruin]

What do you think? The forum rules require you to make an attempt.

(Also, why did you mark your question as solved?)

 

[Cici2017]

What do you think? The forum rules require you to make an attempt.

(Also, why did you mark your question as solved?)

Is it 1/2mω²x²?

 

[Orodruin]

What is your reasoning behind that expression?

 

[Cici2017]

What is your reasoning behind that expression?

Sorry~ I don't know, I just have this equation written down in my notes. Please Hep~

 

[Orodruin]

Sorry~ I don't know, I just have this equation written down in my notes. Please Hep~

So, this actually makes the point I was going for. The equation is correct and will give you the right answer. However, just applying equations blindly is the wrong way of going about to learn physics. You will be much better served by understanding where an expression comes from than trying to memorise a large set of expressions and their range of applicability. If you want to do that, this forum is a great resource for asking for explanations and clarifications. What will generally not happen here is spoonfeeding and replies to the effect of "just use this equation".

If you would like, we can attempt to walk you through the reasoning behind the expression.

 

[Cici2017]

So, this actually makes the point I was going for. The equation is correct and will give you the right answer. However, just applying equations blindly is the wrong way of going about to learn physics. You will be much better served by understanding where an expression comes from than trying to memorise a large set of expressions and their range of applicability. If you want to do that, this forum is a great resource for asking for explanations and clarifications. What will generally not happen here is spoonfeeding and replies to the effect of "just use this equation".

If you would like, we can attempt to walk you through the reasoning behind the expression.

Yes, please.
Does the equation have anything to do with the acceleration= -ω²x?

 

[Orodruin]

Partially, that is how the angular frequency connects into the differential equation.

Let me ask you these questions: How does $\omega$ relate to the mass and the spring constant of the harmonic oscillator? What is the maximal potential energy of the system? What is the minimum potential energy of the system?

If you feel more comfortable solving the differential equation we can do that instead, but I think this is a quicker and more illuminating path.

 

[Orodruin]

Also, do not worry if you cannot answer one of the questions. Just ask about it and I can drop you another hint. The entire goal is to make sure you have a grasp of all steps involved and that includes the underlying ideas and results.

 

[Cici2017]

Partially, that is how the angular frequency connects into the differential equation.

Let me ask you these questions: How does $\omega$ relate to the mass and the spring constant of the harmonic oscillator? What is the maximal potential energy of the system? What is the minimum potential energy of the system?

If you feel more comfortable solving the differential equation we can do that instead, but I think this is a quicker and more illuminating path.

 

[Orodruin]

The relation between the frequency and the mass is correct. However, the potential energy in this problem is due to the extension/compression of the spring, not due to gravity. What is the potential energy of a spring?

 

[Cici2017]

The relation between the frequency and the mass is correct. However, the potential energy in this problem is due to the extension/compression of the spring, not due to gravity. What is the potential energy of a spring?

P=1/2kx²
k=-w²m
P=-1/2w²mx²

 

[Orodruin]

Actually, there is a sign mistake, the force is in the direction opposite to the displacement so k and m have the same sign.

Apart from the sign you have the potential correct. So what is the difference in the potential between the max and min potential? How does this relate to the max and min kinetic energy?