https://fizipedia.bme.hu:80/index.php?title=Mechanika_-_Rezg%C3%A9sek_p%C3%A1lyaegyenlete&feed=atom&action=history
Mechanika - Rezgések pályaegyenlete - Laptörténet
2024-03-28T21:24:51Z
Az oldal laptörténete a wikiben
MediaWiki 1.21.1
https://fizipedia.bme.hu/index.php?title=Mechanika_-_Rezg%C3%A9sek_p%C3%A1lyaegyenlete&diff=13604&oldid=prev
Gombkoto, 2013. november 27., 14:09-n
2013-11-27T14:09:42Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2013. november 27., 14:09-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">12. sor:</td>
<td colspan="2" class="diff-lineno">12. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>#: b) $x=A\sin{\omega t}$ ; $y=A\cos{2\omega t}$</wlatex><includeonly><wlatex>{{Útmutatás|content=Ejtsük ki az időkoordinátát.}}{{Végeredmény|content=$$y^2=4x^2\left(1-\frac{x^2}{A^2}\right)$$ $$y=A\left(1-\frac{2x^2}{A^2}\right)$$}}</wlatex></includeonly><noinclude></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>#: b) $x=A\sin{\omega t}$ ; $y=A\cos{2\omega t}$</wlatex><includeonly><wlatex>{{Útmutatás|content=Ejtsük ki az időkoordinátát.}}{{Végeredmény|content=$$y^2=4x^2\left(1-\frac{x^2}{A^2}\right)$$ $$y=A\left(1-\frac{2x^2}{A^2}\right)$$}}</wlatex></includeonly><noinclude></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Megoldás ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Megoldás ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><wlatex>#: a) $$y^2=4A^2\sin^2{\omega t}\cos^2{\omega t}=4x^2(1-\sin^2{\omega t})=4x^2\left(1-\frac{x^2}{A^2}\right)$$</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><wlatex>#: <ins class="diffchange diffchange-inline">[[Kép:kisfiz1gy-1.4.35M.svg|none|250px]]</ins>a) $$y^2=4A^2\sin^2{\omega t}\cos^2{\omega t}=4x^2(1-\sin^2{\omega t})=4x^2\left(1-\frac{x^2}{A^2}\right)$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>#: b) $$y=A(\cos^2{\omega t}-\sin^2{\omega t})=A(1-2\sin^2{\omega t})=A\left(1-\frac{2x^2}{A^2}\right)$$</wlatex></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>#: b) $$y=A(\cos^2{\omega t}-\sin^2{\omega t})=A(1-2\sin^2{\omega t})=A\left(1-\frac{2x^2}{A^2}\right)$$</wlatex></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></noinclude></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></noinclude></div></td></tr>
</table>
Gombkoto
https://fizipedia.bme.hu/index.php?title=Mechanika_-_Rezg%C3%A9sek_p%C3%A1lyaegyenlete&diff=13602&oldid=prev
Gombkoto, 2013. november 27., 13:46-n
2013-11-27T13:46:23Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2013. november 27., 13:46-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">10. sor:</td>
<td colspan="2" class="diff-lineno">10. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></noinclude><wlatex># (1.4.35.) Határozzuk meg a pont $y=y(x)$ pályaegyenletét, ha a koordináták időfüggése:</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></noinclude><wlatex># (1.4.35.) Határozzuk meg a pont $y=y(x)$ pályaegyenletét, ha a koordináták időfüggése:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>#: a) $x=A\sin{\omega t}$ ; $y=A\sin{2\omega t}$</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>#: a) $x=A\sin{\omega t}$ ; $y=A\sin{2\omega t}$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>#: b) $x=A\sin{\omega t}$ ; $y=A\cos{2\omega t}$</wlatex><includeonly><wlatex>{{Útmutatás|content=Ejtsük ki az időkoordinátát.}}{{Végeredmény|content=$$y=<del class="diffchange diffchange-inline">2x\pm</del>\<del class="diffchange diffchange-inline">sqrt{</del>1-\frac{x^2}{A^2}<del class="diffchange diffchange-inline">}</del>$$ $$y=A\left(1-\frac{2x^2}{A^2}\right)$$}}</wlatex></includeonly><noinclude></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>#: b) $x=A\sin{\omega t}$ ; $y=A\cos{2\omega t}$</wlatex><includeonly><wlatex>{{Útmutatás|content=Ejtsük ki az időkoordinátát.}}{{Végeredmény|content=$$y<ins class="diffchange diffchange-inline">^2</ins>=<ins class="diffchange diffchange-inline">4x^2</ins>\<ins class="diffchange diffchange-inline">left(</ins>1-\frac{x^2}{A^2}<ins class="diffchange diffchange-inline">\right)</ins>$$ $$y=A\left(1-\frac{2x^2}{A^2}\right)$$}}</wlatex></includeonly><noinclude></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Megoldás ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Megoldás ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><wlatex>#: a) $$<del class="diffchange diffchange-inline">\frac </del>y <del class="diffchange diffchange-inline">{2A}</del>=\sin{\omega t}\cos{\omega t}=<del class="diffchange diffchange-inline">\frac xA\pm\sqrt{</del>1-\sin^2{\omega t}<del class="diffchange diffchange-inline">}</del>=\<del class="diffchange diffchange-inline">frac xA\pm\sqrt{</del>1-\frac{x^2}{A^2}<del class="diffchange diffchange-inline">}</del>$$</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><wlatex>#: a) $$y<ins class="diffchange diffchange-inline">^2</ins>=<ins class="diffchange diffchange-inline">4A^2</ins>\sin<ins class="diffchange diffchange-inline">^2</ins>{\omega t}\cos<ins class="diffchange diffchange-inline">^2</ins>{\omega t}=<ins class="diffchange diffchange-inline">4x^2(</ins>1-\sin^2{\omega t}<ins class="diffchange diffchange-inline">)</ins>=<ins class="diffchange diffchange-inline">4x^2</ins>\<ins class="diffchange diffchange-inline">left(</ins>1-\frac{x^2}{A^2}<ins class="diffchange diffchange-inline">\right)</ins>$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>#: b) $$y=A(\cos^2{\omega t}-\sin^2{\omega t})=A(1-2\sin^2{\omega t})=A\left(1-\frac{2x^2}{A^2}\right)$$</wlatex></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>#: b) $$y=A(\cos^2{\omega t}-\sin^2{\omega t})=A(1-2\sin^2{\omega t})=A\left(1-\frac{2x^2}{A^2}\right)$$</wlatex></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></noinclude></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></noinclude></div></td></tr>
</table>
Gombkoto
https://fizipedia.bme.hu/index.php?title=Mechanika_-_Rezg%C3%A9sek_p%C3%A1lyaegyenlete&diff=13599&oldid=prev
Gombkoto, 2013. november 26., 21:35-n
2013-11-26T21:35:30Z
<p></p>
<table class='diff diff-contentalign-left'>
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">←Régebbi változat</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">A lap 2013. november 26., 21:35-kori változata</td>
</tr><tr><td colspan="2" class="diff-lineno">10. sor:</td>
<td colspan="2" class="diff-lineno">10. sor:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></noinclude><wlatex># (1.4.35.) Határozzuk meg a pont $y=y(x)$ pályaegyenletét, ha a koordináták időfüggése:</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></noinclude><wlatex># (1.4.35.) Határozzuk meg a pont $y=y(x)$ pályaegyenletét, ha a koordináták időfüggése:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>#: a) $x=A\sin{\omega t}$ ; $y=A\sin{2\omega t}$</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>#: a) $x=A\sin{\omega t}$ ; $y=A\sin{2\omega t}$</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>#: b) $x=A\sin{\omega t}$ ; $y=A\cos{2\omega t}$</wlatex><includeonly><wlatex>{{Útmutatás|content=Ejtsük ki az időkoordinátát.}}{{Végeredmény|content=$$y=2x\sqrt{1-\frac{x^2}{A^2}}$$ $$y=A\left(1-\frac{2x^2}{A^2}\right)$$}}</wlatex></includeonly><noinclude></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>#: b) $x=A\sin{\omega t}$ ; $y=A\cos{2\omega t}$</wlatex><includeonly><wlatex>{{Útmutatás|content=Ejtsük ki az időkoordinátát.}}{{Végeredmény|content=$$y=2x<ins class="diffchange diffchange-inline">\pm</ins>\sqrt{1-\frac{x^2}{A^2}}$$ $$y=A\left(1-\frac{2x^2}{A^2}\right)$$}}</wlatex></includeonly><noinclude></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Megoldás ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Megoldás ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><wlatex>#: a) $$\frac y {2A}=\sin{\omega t}\cos{\omega t}=\frac xA\sqrt{1-\sin^2{\omega t}}=\frac xA\sqrt{1-\frac{x^2}{A^2}}$$</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><wlatex>#: a) $$\frac y {2A}=\sin{\omega t}\cos{\omega t}=\frac xA<ins class="diffchange diffchange-inline">\pm</ins>\sqrt{1-\sin^2{\omega t}}=\frac xA<ins class="diffchange diffchange-inline">\pm</ins>\sqrt{1-\frac{x^2}{A^2}}$$</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>#: b) $$y=A(\cos^2{\omega t}-\sin^2{\omega t})=A(1-2\sin^2{\omega t})=A\left(1-\frac{2x^2}{A^2}\right)$$</wlatex></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>#: b) $$y=A(\cos^2{\omega t}-\sin^2{\omega t})=A(1-2\sin^2{\omega t})=A\left(1-\frac{2x^2}{A^2}\right)$$</wlatex></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></noinclude></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></noinclude></div></td></tr>
</table>
Gombkoto
https://fizipedia.bme.hu/index.php?title=Mechanika_-_Rezg%C3%A9sek_p%C3%A1lyaegyenlete&diff=6519&oldid=prev
Gombkoto: Új oldal, tartalma: „<noinclude> Kategória:Kísérleti fizika gyakorlat 1. Kategória:Szerkesztő:Gombkötő Kategória:Mechanika {{Kísérleti fizika gyakorlat | tárgynév = …”
2012-11-21T14:50:44Z
<p>Új oldal, tartalma: „<noinclude> <a href="https://fizipedia.bme.hu/index.php?title=Kateg%C3%B3ria:K%C3%ADs%C3%A9rleti_fizika_gyakorlat_1.&action=edit&redlink=1" class="new" title="Kategória:Kísérleti fizika gyakorlat 1. (a lap nem létezik)">Kategória:Kísérleti fizika gyakorlat 1.</a> <a href="https://fizipedia.bme.hu/index.php?title=Kateg%C3%B3ria:Szerkeszt%C5%91:Gombk%C3%B6t%C5%91&action=edit&redlink=1" class="new" title="Kategória:Szerkesztő:Gombkötő (a lap nem létezik)">Kategória:Szerkesztő:Gombkötő</a> <a href="https://fizipedia.bme.hu/index.php/Kateg%C3%B3ria:Mechanika" title="Kategória:Mechanika">Kategória:Mechanika</a> {{Kísérleti fizika gyakorlat | tárgynév = …”</p>
<p><b>Új lap</b></p><div><noinclude><br />
[[Kategória:Kísérleti fizika gyakorlat 1.]]<br />
[[Kategória:Szerkesztő:Gombkötő]]<br />
[[Kategória:Mechanika]]<br />
{{Kísérleti fizika gyakorlat<br />
| tárgynév = Kísérleti fizika gyakorlat 1.<br />
| témakör = Mechanika - Rezgések I.<br />
}}<br />
== Feladat ==<br />
</noinclude><wlatex># (1.4.35.) Határozzuk meg a pont $y=y(x)$ pályaegyenletét, ha a koordináták időfüggése:<br />
#: a) $x=A\sin{\omega t}$ ; $y=A\sin{2\omega t}$<br />
#: b) $x=A\sin{\omega t}$ ; $y=A\cos{2\omega t}$</wlatex><includeonly><wlatex>{{Útmutatás|content=Ejtsük ki az időkoordinátát.}}{{Végeredmény|content=$$y=2x\sqrt{1-\frac{x^2}{A^2}}$$ $$y=A\left(1-\frac{2x^2}{A^2}\right)$$}}</wlatex></includeonly><noinclude><br />
== Megoldás ==<br />
<wlatex>#: a) $$\frac y {2A}=\sin{\omega t}\cos{\omega t}=\frac xA\sqrt{1-\sin^2{\omega t}}=\frac xA\sqrt{1-\frac{x^2}{A^2}}$$<br />
#: b) $$y=A(\cos^2{\omega t}-\sin^2{\omega t})=A(1-2\sin^2{\omega t})=A\left(1-\frac{2x^2}{A^2}\right)$$</wlatex><br />
</noinclude></div>
Gombkoto