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Cici2017
Homework Statement
Homework Equations
The Attempt at a Solution
What do I do next to work out kinetic energy?
How do I calculate kinetic energy in oscillation problems?
- Thread starter Cici2017
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SUMMARY
The discussion centers on calculating kinetic energy in oscillation problems, specifically using the equation KE = 1/2 mω²x². Participants emphasize the importance of understanding the derivation of this equation rather than memorizing it. The relationship between angular frequency (ω), mass (m), and spring constant (k) in harmonic oscillators is also explored, highlighting the connection between potential energy (P = 1/2 kx²) and kinetic energy. The conversation encourages a deeper comprehension of the underlying physics principles involved in oscillatory motion.
PREREQUISITES- Understanding of harmonic oscillators and their equations
- Familiarity with angular frequency (ω) and its significance
- Knowledge of potential energy in springs (P = 1/2 kx²)
- Basic concepts of kinetic energy in physics
- Study the derivation of the kinetic energy equation in oscillatory systems
- Learn about the relationship between angular frequency, mass, and spring constant
- Explore the concepts of potential and kinetic energy in harmonic motion
- Investigate differential equations related to oscillatory motion
Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to enhance their teaching methods in these topics.
What do I do next to work out kinetic energy?
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What do you think? The forum rules require you to make an attempt.
(Also, why did you mark your question as solved?)
(Also, why did you mark your question as solved?)
- #3
Cici2017
Is it 1/2mω2x2?Orodruin said:
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What is your reasoning behind that expression?
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Cici2017
Sorry~ I don't know, I just have this equation written down in my notes. Please Hep~Orodruin said:
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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".Cici2017 said:Sorry~ I don't know, I just have this equation written down in my notes. Please Hep~
If you would like, we can attempt to walk you through the reasoning behind the expression.
- #7
Cici2017
Yes, please.Orodruin said:
Does the equation have anything to do with the acceleration= -ω2x?
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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.
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.
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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.
- #10
Cici2017
Orodruin said:
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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?
- #12
Cici2017
P=1/2kx2Orodruin said:
k=-w2m
P=-1/2w2mx2
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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?
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?