CLS-30

SHO energy

Amplitude energy of a spring.

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GoverningSHO energy

Governing equation

E=\tfrac12 k A^2

$A \in \left[0.01, 0.5\right]$

where

k: k (N/m)
A: A (m)
E: SHO energy (J)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

E=\tfrac12 k A^2

$A \in \left[0.01, 0.5\right]$

$A = 0.01$ $E = 0.002$

Along the curve

②

Domain of the variable — blue

A_{\min} = 0.01,\quad A_{\max} = 0.5

$A \in \left[0.01, 0.5\right]$

$A = 0.01$ $A = 0.01$

Along the curve

③

Response curve — green

E=\tfrac12 k A^2

$A \in \left[0.01, 0.5\right]$

$A = 0.01$ $E = 0.002$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E}{\mathrm{d}A}

$A \in \left[0.01, 0.5\right]$

$A = 0.013$ $E^{\prime} = 0.523$

Along the curve

Lecture brief

Historical brief

Newtonian mechanics (1687) plus energy, angular momentum, Kepler and the ballistic parabola remain the first language of motion. Every sheet here is a closed-form orbit, throw, spin or oscillator. This sheet (CLS-30 — SHO energy) is the form associated with SHO energy. Working symbols: $k$ , $A$ $\rightarrow$ $E$ . Amplitude energy of a spring. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

E

from

k

A

in Classical mechanics via

E=\tfrac12 k A^2

Amplitude energy of a spring. Use it when a real classical mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

k = 40.000\,\mathrm{N/m}

A = 0.080\,\mathrm{m}

, the governing relation

E=\tfrac12 k A^2

yields

E = 0.128\,\mathrm{J}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

k k40 N/mA A0.08 m

Outputs

SHO energy E0.128 J

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Amplitude energy of a spring. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube