# What is the maximum potential energy of an oscillating mass?

• lussi
In summary, at the equilibrium point the potential energy is equal to 1/2 kx2. At the max position the potential energy is 25 J.
lussi
1. Homework Statement
A 2-kg mass attached to a spring oscillates in simple harmonic motion and has a speed of 5 m/s at the equilibrium point. What is the maximum potential energy of this oscillating mass?

2. Homework Equations
I know that the potential energy is: Ep = 1/2 kx2
k = mω2

In SHM,

KE+PE = Constant.

At the equilibrium position, the PE is what value? Once you have that then at the max position of the spring, the KE is what value?

So, at the equilibrium position KE = PE, therefore KE = 1/2 mv2 = 25 J. And PE = 25 J. If that's correct. But I don't know what will be the value at the max position

Not that KE= PE. It is that KE+PE= a constant. So, you can (for example), find all the different energies at the equilibrium and then find all the energies at your maximum potential. And then you know that they must equal the same constant (in the end you should only have max PE which you don't know).

I really don't know how to do it, and I have an exam tomorrow. If you tell me the solution, I might find the logic by looking at it.

lussi said:
I really don't know how to do it, and I have an exam tomorrow. If you tell me the solution, I might find the logic by looking at it.

KE +PE = Constant

At the equilibrium position you found that PE=0 so that KE = Constant = 25 J

Therefore

KE+PE = 25

At the maximum positionm what would be the KE? (when the spring is oscillating after it reaches its max position does it keep going or does its velocity change?)

Since KE + PE = const, and at the equilibrium position PE = 0, therefore KE = Constant = 25 J, as you rock.freak667 said. And since "they must equal the same constant", as Jufro said, that means that at the maximum position KE = 0 and PE = const = 25 J. Is that correct, or am I mistaken again?

lussi said:
Since KE + PE = const, and at the equilibrium position PE = 0, therefore KE = Constant = 25 J, as you rock.freak667 said. And since "they must equal the same constant", as Jufro said, that means that at the maximum position KE = 0 and PE = const = 25 J. Is that correct, or am I mistaken again?

Yes that is correct. So PE=25 J at the max position.

For SHM KE+PE = constant at any point in the motion

Thank you very much :)

## 1. What is potential energy?

Potential energy is a form of energy that an object possesses due to its position or configuration in a system. It is the energy that an object has the potential to convert into other forms of energy, such as kinetic energy.

## 2. What is an oscillating mass?

An oscillating mass refers to a mass that is moving back and forth between two points in a periodic motion. This can occur in various systems, such as a pendulum or a spring. The mass's potential energy changes as it oscillates between these points.

## 3. How is the maximum potential energy of an oscillating mass calculated?

The maximum potential energy of an oscillating mass can be calculated using the formula: E = 1/2kA^2, where E is the maximum potential energy, k is the spring constant, and A is the amplitude of the oscillation. This formula assumes that the oscillation is a simple harmonic motion.

## 4. What factors affect the maximum potential energy of an oscillating mass?

The maximum potential energy of an oscillating mass is affected by the mass's amplitude, the spring constant, and the mass's initial position. It also depends on the type of oscillation, as some types of oscillation have a different formula for calculating potential energy.

## 5. Can the maximum potential energy of an oscillating mass be greater than its initial potential energy?

Yes, it is possible for the maximum potential energy of an oscillating mass to be greater than its initial potential energy. This can occur when the amplitude of the oscillation is larger than the initial displacement of the mass, resulting in a greater potential energy at the maximum point of the oscillation.

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