弹簧振子的简谐运动演示
2020-05-11 12:31
本范例演示弹簧振子的简谐运动过程。通过参数方程与三角函数（正弦/余弦）构建弹簧与质点的运动轨迹，直观展示位移随时间呈周期性变化的规律。利用 CurveCartesian 命令绘制运动曲线，结合滑块动画实时呈现弹簧伸缩与振子往复运动的动态效果，帮助理解简谐运动的数学本质及其函数图像特征。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.580.0" app="classic" platform="d" id="1b49c32c-08c2-434a-8568-027aae8cf1d8" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="1456" height="876" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.17925824175824176" orientation="1" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="527,394,700,550" />
<view id="1" visible="false" inframe="false" stylebar="false" location="1,3" size="1204" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="true" location="1,3" size="300" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="false" location="3" size="261" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="true" inframe="false" stylebar="true" location="1" size="1429" window="100,100,600,400" />
</views>
<toolbar show="false" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="true" east="true" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="1204" height="888"/>
<coordSystem xZero="684.9999999999999" yZero="414.0" scale="49.99999999999998" yscale="50.00000000000001"/>
<evSettings axes="true" grid="true" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<algebraView>
<mode val="1"/>
<auxiliary show="true"/>
</algebraView>
<kernel>
<uses3D val="true"/>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
<startAnimation val="true"/>
</kernel>
<tableview min="-2.0" max="2.0" step="1.0"/>
<scripting blocked="false" disabled="false"/>
<euclidianView3D>
<coordSystem xZero="0.0" yZero="0.0" zZero="-1.4999999999999996" scale="56.175064945180104" xAngle="8.0" zAngle="630.2509809512536"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" gridType="3"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="2" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<plate show="false"/>
<bgColor r="255" g="255" b="255"/>
<clipping use="false" show="false" size="1"/>
<projection type="0"/>
</euclidianView3D>
<construction title="" author="" date="">
<expression label="a" exp="(x - 5)^(2) + (z - 6)^(2) = 4" type="quadric"/>
<element type="quadric" label="a">
<show object="false" label="false" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="0.0" x1="0.0" y1="0.0" z1="-1.0" x2="0.0" y2="1.0" z2="0.0"/>
<matrix A0="1.0" A1="0.0" A2="1.0" A3="57.0" A4="0.0" A5="0.0" A6="0.0" A7="-5.0" A8="0.0" A9="-6.0"/>
<eqnStyle style="implicit"/>
</element>
<expression label="b" exp="y = 0" type="plane"/>
<element type="plane3d" label="b">
<show object="false" label="false" ev="4"/>
<objColor r="99" g="219" b="219" alpha="0.5"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0.0" y="1.0" z="0.0" w="0.0"/>
<fading val="0.1"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
</element>
<command name="IntersectPath">
<input a0="b" a1="a"/>
<output a0="d"/>
</command>
<element type="conic3d" label="d">
<show object="false" label="true" ev="4"/>
<objColor r="255" g="127" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="1.0" x1="-0.0" y1="1.0" z1="1.0"/>
<matrix A0="1.0" A1="1.0" A2="57.0" A3="0.0" A4="5.0" A5="6.0"/>
<eqnStyle style="parametric"/>
</element>
<command name="Point">
<input a0="d"/>
<output a0="A"/>
</command>
<element type="point3d" label="A">
<show object="false" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="6" type="1" playing="true"/>
<coords x="6.9645745014462825" y="0.0" z="6.374762629229612" w="1.0"/>
<pointSize val="5"/>
</element>
<expression label="c" exp="x(A)" />
<element type="numeric" label="c">
<value val="6.9645745014462825"/>
<symbolic val="true" />
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<expression label="f" exp="f(t) = (0.5 * sin((80 * t / c)))" />
<element type="function" label="f">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
</element>
<expression label="g" exp="g(t) = (0.5 * cos((80 * t / c)))" />
<element type="function" label="g">
<show object="false" label="false" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
</element>
<expression label="h" exp="h(t) = t" type="function"/>
<element type="function" label="h">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
</element>
<expression label="球" exp="(x - c)^(2) + y^(2) + z^(2) = 1.25" type="quadric" />
<element type="quadric" label="球">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="51" alpha="0.75"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<eigenvectors x0="1.0" y0="0.0" z0="0.0" x1="0.0" y1="1.0" z1="0.0" x2="0.0" y2="0.0" z2="1.0"/>
<matrix A0="1.0" A1="1.0" A2="1.0" A3="47.255297986195735" A4="0.0" A5="0.0" A6="0.0" A7="-6.9645745014462825" A8="0.0" A9="0.0"/>
<eqnStyle style="specific"/>
</element>
<command name="CurveCartesian">
<input a0="h(t)" a1="f(t)" a2="g(t)" a3="t" a4="0" a5="c - 1"/>
<output a0="弹簧"/>
</command>
<element type="curvecartesian3d" label="弹簧">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelOffset x="-1" y="1"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
</element>
<expression label="e" exp="x = 0" type="plane"/>
<element type="plane3d" label="e">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="1.0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<coords x="1.0" y="0.0" z="0.0" w="0.0"/>
<fading val="0.1"/>
<lineStyle thickness="0" type="0" typeHidden="1"/>
<eqnStyle style="user"/>
</element>
<expression label="text1" exp=""按住右鼠标键，可旋转3D视图 ""/>
<element type="text" label="text1">
<show object="true" label="false" ev="37"/>
<objColor r="0" g="0" b="0" alpha="0.0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="2.0" size="12" style="1"/>
<absoluteScreenLocation x="59" y="319"/>
</element>
</construction>
</geogebra>