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Concept module

Oscillation Energy

Watch kinetic and potential energy trade places in simple harmonic motion while the total stays fixed by amplitude and spring stiffness.

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Starter track

Step 2 of 30 / 3 complete

Oscillations and Energy

Earlier steps still set up Oscillation Energy.

1. Simple Harmonic Motion2. Oscillation Energy3. Damping / Resonance

Previous step: Simple Harmonic Motion.

Start from track beginning

Why it behaves this way

Explanation

Oscillation energy is the same simple harmonic motion you already know, but viewed through what the system stores and releases. The mass never loses total energy in the ideal model; it keeps trading that energy between spring potential energy and kinetic energy.

That exchange is easiest to trust when the motion, the bars, and the graph stay locked together. The goal here is to see why turning points are pure potential-energy moments, why equilibrium is the kinetic-energy peak, and how amplitude and spring stiffness set the total-energy scale.

Key ideas

01At the turning points, velocity is zero, so kinetic energy is zero and the spring stores all of the energy as potential energy.

02At equilibrium, displacement is zero, so spring potential energy is minimal and the motion carries almost all of the energy as kinetic energy.

03In ideal SHM, the total-energy line stays flat while kinetic and potential energy trade places.

04Changing amplitude or spring constant changes the total stored energy, while changing phase only changes where the cycle starts.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Solve the energy state that is actually on screen. Freeze it if you want a stable snapshot, or keep it live and let the example follow the motion.

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Frozen valuesFrozen at 0.00

At $t = 0 s$ , how is the oscillator's total energy split between kinetic and potential energy?

t

Time

0 s

m

Mass

1 kg

k

Spring constant

3.2 N/m

x

Current displacement

0.87 m

v

Current velocity

-1.96 m/s

1. Write the two energy relations

Use

K = \frac{1}{2} m v^{2}

and

U = \frac{1}{2} k x^{2}

for the same instant.

2. Substitute the live values

K = \frac{1}{2} (1) (- 1.96)^{2}

and

U = \frac{1}{2} (3.2) (0.87)^{2}

3. Compare the two parts

That gives

K = 1.92 J

and

U = 1.21 J

, so the total stays

E = 3.14 J

Energy at this instant

K = 1.92 J, U = 1.21 J, E = 3.14 J

Kinetic energy is larger here, so the mass is in the faster middle part of the swing rather than near an edge.

Common misconception

If the mass stops for an instant at a turning point, the oscillator has no energy there.

The motion stops only because the energy is temporarily stored in the spring instead of in the mass's motion.

At the turning point, kinetic energy is zero but potential energy is at its maximum, so the total energy is still present and ready to pull the system back.

Mini challenge

Two oscillators have the same amplitude, mass, and spring constant. One starts at equilibrium and the other starts at a turning point. Which one has more total energy?

Make a prediction before you reveal the next step.

Decide whether starting position changes the total energy or only changes how that same total is split between kinetic and potential energy.

Check your reasoning against the live bench.

They have the same total energy. The starting position only changes the split between kinetic and potential energy.

Amplitude and spring constant set the total-energy scale in ideal SHM. Phase only changes where the cycle begins, so one oscillator can start as pure kinetic while the other starts as pure potential even though the total is the same.

Quick test

Graph reading

Question 1 of 4

Answer from the motion and the energy meaning together. These checks are about what must be true, not about plugging numbers into a formula by habit.

At the instant the mass crosses equilibrium in this ideal oscillator, what must the energy graph show?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows a single oscillator moving back and forth across an equilibrium point. Optional markers show the turning points, and an energy card shows how the total energy is split between kinetic and spring potential energy at the current instant.

Changing amplitude, spring constant, mass, or phase updates the same motion, the same energy readout, and the same graph so the energy story stays tied to one physical state.

Graph summary

The energy graph shows kinetic, potential, and total energy as synchronized views of the same oscillation. The displacement and velocity graphs sit beside it so you can compare where the mass is, how fast it is moving, and which energy form is dominating.

Pausing or scrubbing the graph keeps the stage, the energy bars, and the marker locked to the same instant.

Keep this idea moving

Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Boundary patternOscillations

Oscillation Energy

Oscillations and Energy

Explanation

Step through the frozen example

At $t = 0 s$ , how is the oscillator's total energy split between kinetic and potential energy?

At the instant the mass crosses equilibrium in this ideal oscillator, what must the energy graph show?

Keep this idea moving

Standing Waves

Wave Interference

Damping / Resonance

Oscillation Energy

Oscillations and Energy

Explanation

Step through the frozen example

At t=0s, how is the oscillator's total energy split between kinetic and potential energy?

At the instant the mass crosses equilibrium in this ideal oscillator, what must the energy graph show?

Keep this idea moving

Standing Waves

Wave Interference

Damping / Resonance

At $t = 0 s$ , how is the oscillator's total energy split between kinetic and potential energy?