Kinetic and Potential Energy in Simple Harmonic Motion

AI Thread Summary
The discussion centers on understanding kinetic and potential energy in simple harmonic motion for a 3.0 kg object with a total energy of 0.4 J. Participants express confusion about calculating potential energy at a displacement of +4 cm, noting that their results exceed the total energy, indicating a possible error in displacement usage. Questions arise regarding the maximum displacement along the x-axis and the relationship between potential and kinetic energy, with emphasis on the need for clarity on whether displacement refers to the x or y component. Additionally, there is uncertainty about calculating kinetic energy and speed without knowing acceleration or time. The conversation highlights the importance of correctly interpreting the problem's parameters and units to solve for energy values accurately.
Tabe
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Kinetic and Potential Energy?

This problem is totally confusing me..can someone please explain it...:confused:

A 3.0 kg object subject to a restoring force F is undergoing simple harmonic motion with a small amplitude. The potential energy U of the object as a function of distance x from its equilibrium is shown. This particular object has a total energy E: of 0.4 J.

(a) What is the object's potential energy when its displacement is +4 cm from its equilibrium position?
For this problem, I used 4 cm as my displacement, but when I used it in the formula, I ended up getting an answer that is greater than the total energy, so I know it must be wrong. Am I using the wrong displacement?

(b) What is the farthest the object moves along the x-axis in the positive direction? Explain.
I really don't understand how to solve for the distand in the x-axis without having the acceleration or time. Is there a formula that I've overlooked or am I just making this problem more complicated than it is?

(c) Determine the object's kinetic energy when its displacement is -7 cm.
For this part, the kinetic energy equation is KE= 1/2mv^2. How do I solve for the velocity without time or acceleration?

(d) What is the object's speed at x= 0?
Again, I would need the answers from (c) to solve for the speed.
 
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Is there an image?
The potential energy U of the object as a function of distance x from its equilibrium is shown
 
For part 9 (a). Mind your units. The units for Joules is: 1 Joule = 1 kgm^2/s^2.
If you are using cm, you will not be getting Joules, but rather "centi-Joules" :P

For part (b). The energy of a oscillator can be expressed as the sum of it's potential (1/2kx^2) and kinetic (1/2mv^2). At max displacement, it has zero kinetic energy.
 
There is a graph of the distance and potential energy. When the problem states that it is 4cm from its equilibrium position, is it referring to the x or y component?
 
Tabe said:
When the problem states that it is 4cm from its equilibrium position, is it referring to the x or y component?

I believe we are talking about a 1 dimensional oscillator, and that dimension is the x?
 

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