# Oscillator with equal amounts of kinetic and potential energy

• Dwrigh08
In summary, the conversation is discussing a simple harmonic oscillator with a spring of force constant 5.79 N/m and a mass of 0.828 kg. The oscillator is initially displaced 3.5 cm from equilibrium and the question is asking for the distance from equilibrium where the oscillator will have equal amounts of kinetic and potential energy. The student attempts to solve the problem using equations for kinetic and potential energy, but struggles and asks for help. Another student provides the correct equations and advises to set the kinetic and potential energy equal to each other and solve for x.
Dwrigh08

## Homework Statement

If you have a simple harmonic oscillator based on a spring of force constant 5.79 N/m, with an attached mass of 0.828 kg, and the oscillator is initially displaced 3.5 cm from equilibrium, at what distance from the equilibrium point (in cm) will the oscillator have equal amounts of kinetic and potential energy?

## Homework Equations

I am using Kinetic energy=1/2 mass x omega^2 and Potential energy= 1/2 spring constant x displacement^2 and omega= root of (spring constant/ mass)

## The Attempt at a Solution

My first thought was to set the kinetic energy and pitential equal to each other and solve for the displacement. When I try to do this I end up with 1. My next thought was to take into account the initial displacement and subtract that from 1. Neither work for me. I feel like i am missing an obvious step. Any help would be appreciated.

Can you wright down the expressions for kinetic energy and potential energy for a SHM in terms of k, amplitude and displacement?

I know that total energy= 1/2 k A^2. I tried to solve for total energy and then using E= K+U and rewriting E= 1/2 m w^2 + 1/2 k x^2. I come out with an energy from the first equation and then try to solve for x using the second equation. I don't think that is the right approach.

In SHM, at any instant, the kinetic energy = 1/2*m*w^2(A^2-x^2) = 1/2*k*(A^2-x^2)and potential energy = 1/2*k*x^2
Equate KE = PE and solve for x.

## 1. What is an oscillator with equal amounts of kinetic and potential energy?

An oscillator with equal amounts of kinetic and potential energy is a type of system where the total energy is evenly divided between kinetic energy (energy of motion) and potential energy (energy of position). This means that the system is constantly transitioning between kinetic and potential energy as it oscillates or vibrates.

## 2. How does an oscillator with equal amounts of kinetic and potential energy work?

An oscillator with equal amounts of kinetic and potential energy works by converting energy between kinetic and potential forms as it oscillates. As the system moves towards its equilibrium position, potential energy increases while kinetic energy decreases. Then, as the system moves away from equilibrium, potential energy decreases while kinetic energy increases. This cycle continues as long as the oscillator is in motion.

## 3. What is the significance of having equal amounts of kinetic and potential energy in an oscillator?

The significance of having equal amounts of kinetic and potential energy in an oscillator is that it allows for a consistent and balanced oscillation. This means that the system will continue to oscillate at a constant frequency and amplitude without losing or gaining energy. It also allows for a more stable and predictable motion.

## 4. What factors affect the amounts of kinetic and potential energy in an oscillator?

The amounts of kinetic and potential energy in an oscillator are affected by factors such as the amplitude (maximum displacement from equilibrium), frequency (number of oscillations per unit of time), and mass of the system. These factors can change the distribution of energy between kinetic and potential forms, but the total energy remains constant.

## 5. What are some real-life examples of oscillators with equal amounts of kinetic and potential energy?

Some real-life examples of oscillators with equal amounts of kinetic and potential energy include a pendulum, a mass on a spring, and a swinging child on a swing. In all of these systems, the total energy is divided between kinetic and potential forms as the system oscillates back and forth. This phenomenon can also be observed in other natural processes, such as waves and vibrations in molecules.

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