Physics · Oscillations

Oscillation Energy

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Wrap-up

What you learned

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Read next: Damping / ResonanceWatch energy leave or build up

Key takeaway

Kinetic and spring potential energy trade places while total mechanical energy stays fixed in ideal SHM.
Equilibrium crossings are mostly kinetic-energy states; turning points are spring-potential-energy states.
Amplitude and spring constant set the stored total through E = 1/2 k A^2.
Mass changes timing and phase changes the starting split, but neither changes total energy when A and k stay fixed.

Common misconception

Do not say the oscillator has no energy when it stops at a turning point. The energy has moved into spring stretch.

At the turning point, the mass has zero kinetic energy, not zero total energy.

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Boundary patternWaves

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Equation snapshotEnergy handoff snapshot · Potential energyShow 3 equations

Keep kinetic, spring potential, and total energy together so the bars and graph read like one live state.

Energy handoff snapshot
$K = \frac{1}{2} m v^{2}$
Kinetic energy is carried by the moving mass, so it is largest when speed is largest and zero at the turning points.
Potential energy
$U = \frac{1}{2} k x^{2}$
Spring potential energy is stored in stretch or compression, so it is largest at the turning points and smallest at equilibrium.
Total energy
$E = K + U = \frac{1}{2} k A^{2}$
In ideal SHM, the total stays constant while kinetic and potential energy trade places.

Why it behaves this way

Explanation

Oscillation energy is simple harmonic motion viewed through where the energy is stored. In the ideal model, the total energy stays constant, but it changes form as the motion continues.

When the mass is far from equilibrium, the spring is stretched or compressed and stores most of the energy as potential energy. When the mass passes through equilibrium, the spring is least stretched and the motion carries most of the energy as kinetic energy.

The stage, energy bars, and graphs all show the same instant. At a turning point, the mass stops, so kinetic energy is zero and the spring holds the full total energy. At an equilibrium crossing, speed is greatest, so kinetic energy is largest and spring potential energy is smallest.

Use the controls one idea at a time. Amplitude sets the turning points and the total-energy scale, Spring constant changes both the energy scale and the cycle rate, Mass changes the timing, and Phase changes only where the cycle begins.

Key ideas

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

02At equilibrium, displacement is zero, potential energy is smallest, and the oscillator carries almost all of its energy as kinetic energy.

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

04Amplitude and spring constant set the total-energy scale. Phase changes only the starting point, and mass changes the timing rather than the total energy when amplitude and spring constant stay fixed.

Worked examples

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Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the live oscillator as evidence. First read how the total energy is split at the current instant. Then calculate the total energy from the current amplitude and spring constant, and check that the graph keeps that total fixed while kinetic and potential energy trade places.

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Example 1 of 2

Frozen valuesFrozen at 0.00

At $t = 0 s$ , how much of the oscillator's total energy is kinetic and how much is spring potential?

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 kinetic- and potential-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 for the same instant

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

and

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

3. Compare the energy split

That gives

K = 1.92 J

and

U = 1.21 J

, so the total stays

E = 3.14 J

Kinetic, potential, and total energy

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.

Quick test

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Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

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 together, 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 dominant.

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

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Oscillations and Energy

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