Amplitude-Square Energy Three-Row Scan - Waves, Oscillations, and Resonance Step by Step

Holding the spring constant fixed makes the total energy scale with amplitude squared.

Holding the spring constant fixed makes the total energy scale with amplitude squared. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Two-metre amplitude stores four joules

With spring constant 2 newtons per metre and center position, amplitude 2 m gives total energy 4 J.

E={1\over 2}kA^{2}={1\over 2}\times2\times2^{2}=4

Doubling amplitude makes four times the energy

With spring constant 2 newtons per metre and center position, amplitude 4 m gives total energy 16 J.

E={1\over 2}kA^{2}={1\over 2}\times2\times4^{2}=16

Three times the amplitude makes nine times the energy

With spring constant 2 newtons per metre and center position, amplitude 6 m gives total energy 36 J.

E={1\over 2}kA^{2}={1\over 2}\times2\times6^{2}=36