Plot of the steady-state amplitude <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A/A_{\mathrm {stat} }}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">s</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi></mrow></mrow></msub></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle A/A_{\mathrm {stat} }}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03e815706872bfd1ef507fa45f9c72668d5caebf" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:7.63ex; height:2.843ex;" alt="{\displaystyle A/A_{\mathrm {stat} }}"></span> of a <a href="https://en.wikipedia.org/wiki/Harmonic_oscillator#Driven_harmonic_oscillators" class="extiw" title="en:Harmonic oscillator">damped driven oscillator</a> with different damping ratios <i>ζ</i>. The relative driving frequency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \eta =\omega /\omega _{0}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>η<!-- η --></mi><mo>=</mo><mi>ω<!-- ω --></mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><msub><mi>ω<!-- ω --></mi><mrow class="MJX-TeXAtom-ORD"><mn>0</mn></mrow></msub></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \eta =\omega /\omega _{0}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04935baf1777262fea82a3bed57b89988b84d6e3" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:9.376ex; height:2.843ex;" alt="{\displaystyle \eta =\omega /\omega _{0}}"></span> is plotted in the interval [0, 3]. Additionally the envelope and line of maxima is plotted:
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A/A_{stat}={\frac {1}{\sqrt {(1-\eta ^{2})^{2}+(2\eta \zeta )^{2}}}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mi>t</mi><mi>a</mi><mi>t</mi></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><msqrt><mo stretchy="false">(</mo><mn>1</mn><mo>−<!-- − --></mo><msup><mi>η<!-- η --></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>+</mo><mo stretchy="false">(</mo><mn>2</mn><mi>η<!-- η --></mi><mi>ζ<!-- ζ --></mi><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></msqrt></mfrac></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle A/A_{stat}={\frac {1}{\sqrt {(1-\eta ^{2})^{2}+(2\eta \zeta )^{2}}}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/402c24c422e9fc1021e7a5922e081653a909523b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.171ex; width:32.193ex; height:6.509ex;" alt="{\displaystyle A/A_{stat}={\frac {1}{\sqrt {(1-\eta ^{2})^{2}+(2\eta \zeta )^{2}}}}}"></span></dd>
<dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \zeta \in [0.1,0.2,0.3,0.5,1]}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>ζ<!-- ζ --></mi><mo>∈<!-- ∈ --></mo><mo stretchy="false">[</mo><mn>0.1</mn><mo>,</mo><mn>0.2</mn><mo>,</mo><mn>0.3</mn><mo>,</mo><mn>0.5</mn><mo>,</mo><mn>1</mn><mo stretchy="false">]</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \zeta \in [0.1,0.2,0.3,0.5,1]}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a16b8a88ff73d9d08e77bb365b8bbd2bba792743" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:22.415ex; height:2.843ex;" alt="{\displaystyle \zeta \in [0.1,0.2,0.3,0.5,1]}"></span></dd>
<dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{env}/A_{stat}={\frac {1}{|1-\eta ^{2}|}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>e</mi><mi>n</mi><mi>v</mi></mrow></msub><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mi>t</mi><mi>a</mi><mi>t</mi></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><mrow><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow><mn>1</mn><mo>−<!-- − --></mo><msup><mi>η<!-- η --></mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mrow class="MJX-TeXAtom-ORD"><mo stretchy="false">|</mo></mrow></mrow></mfrac></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle A_{env}/A_{stat}={\frac {1}{|1-\eta ^{2}|}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04e62b0e930597f1fa85b577b7d43fd1b14b7329" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.671ex; width:21.95ex; height:6.009ex;" alt="{\displaystyle A_{env}/A_{stat}={\frac {1}{|1-\eta ^{2}|}}}"></span></dd>
<dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{max}/A_{stat}={\frac {1}{\sqrt {1-\eta ^{4}}}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>m</mi><mi>a</mi><mi>x</mi></mrow></msub><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><msub><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mi>s</mi><mi>t</mi><mi>a</mi><mi>t</mi></mrow></msub><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mn>1</mn><msqrt><mn>1</mn><mo>−<!-- − --></mo><msup><mi>η<!-- η --></mi><mrow class="MJX-TeXAtom-ORD"><mn>4</mn></mrow></msup></msqrt></mfrac></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle A_{max}/A_{stat}={\frac {1}{\sqrt {1-\eta ^{4}}}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e956579164c5783e03977cb30183259aa26cac1e" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.171ex; width:23.683ex; height:6.509ex;" alt="{\displaystyle A_{max}/A_{stat}={\frac {1}{\sqrt {1-\eta ^{4}}}}}"></span></dd></dl>
English label version.
<a href="//commons.wikimedia.org/wiki/User:Geek3" title="User:Geek3">Geek3</a>
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