[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2pl\/wiki27\/forma-mechaniczna-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2pl\/wiki27\/forma-mechaniczna-wikipedia\/","headline":"Forma mechaniczna – Wikipedia","name":"Forma mechaniczna – Wikipedia","description":"before-content-x4 Artyku\u0142 w Wikipedii, Free L’Encyclop\u00e9i. after-content-x4 Table of Contents after-content-x4 We wsp\u00f3\u0142rz\u0119dnych kartezja\u0144skich [[[ modyfikator |. Modyfikator i kod","datePublished":"2022-03-22","dateModified":"2022-03-22","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2pl\/wiki27\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2pl\/wiki27\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c94504edbc5ad516587497ee9dc288df8337ea3d","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/c94504edbc5ad516587497ee9dc288df8337ea3d","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2pl\/wiki27\/forma-mechaniczna-wikipedia\/","wordCount":8515,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4Artyku\u0142 w Wikipedii, Free L’Encyclop\u00e9i.          (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Table of Contents       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4We wsp\u00f3\u0142rz\u0119dnych kartezja\u0144skich [[[ modyfikator |. Modyfikator i kod ] We wsp\u00f3\u0142rz\u0119dnych cylindrycznych [[[ modyfikator |. Modyfikator i kod ] We wsp\u00f3\u0142rz\u0119dnych sferycznych [[[ modyfikator |. Modyfikator i kod ] Niekt\u00f3re si\u0142y [[[ modyfikator |. Modyfikator i kod ] Podstawowa zasada dynamiki [[[ modyfikator |. Modyfikator i kod ] Energia potencjalna dla niekt\u00f3rych si\u0142 konserwatywnych [[[ modyfikator |. Modyfikator i kod ] Oscylator harmoniczny (bez t\u0142umienia) [[[ modyfikator |. Modyfikator i kod ] Oscylator z wsp\u00f3\u0142czynnikiem t\u0142umienia L [[[ modyfikator |. Modyfikator i kod ] We wsp\u00f3\u0142rz\u0119dnych kartezja\u0144skich [[[ modyfikator |. Modyfikator i kod ] r= X ux+ I uy+ z uz{DisplayStyle {BoldSymbol {r}} = x {boldsymbol {u}} _ {x}+y {boldsymbol {u}} _ {y}+z {boldsymbol {u}} _ {z}}}}}}}}}}}}}}}}}}}}}} Pr\u0119dko\u015b\u0107 punktu znajduj\u0105ca si\u0119 w R jest napisane v( r) = drdt= dxdtux+ dydtuy+ dzdtuz{DisplayStyle {BoldSymbol {v}} ({BoldSymbol {r}}) = {frac {{text {d}} {boldsymbol {r}}} {{text {d}} t}} = {frac {{text {boldsymbol {r}}} d}} x} {{text {d}} t}} {boldsymbol {u}} _ {x}+{frac {{text {d}} y} {{text {d}} t}} {boldsymbol {boldsymbol {boldsymbol {boldsymbol {boldsymbol { u}} _ {y}+{frac {{text {d}} z} {{text {d}} t}} {BoldSymbol {u}} _ {z}} W i przyspieszenie        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4a( r) = dvdt= d2rdt2= d2xdt2ux+ d2ydt2uy+ d2zdt2uz{DisplayStyle {BoldSymbol {A}} ({BoldSymbol {r}}) = {frac {{text {d}} {boldsymbol {v}}} {{text {d}} t}} = {frac {{text {text {text {boldsymbol {v}}} d}}^{2} {BoldSymbol {r}}} {{text {d}} t^{2}}} = {frac {{text {d}}^{2} x} {{text {d} } t^{2}}} {BoldSymbol {u}} _ {x}+{frac {{text {d}}^{2} y} {{text {d}} t^{2}}} {boldsymbol {u}} _ {y}+{frac {{text {d}}^{2} z} {{text {d}} t^{2}}} {BoldSymbol {u}} _ {z}} . We wsp\u00f3\u0142rz\u0119dnych cylindrycznych [[[ modyfikator |. Modyfikator i kod ] r= R u\u03c1+ z uz{DisplayStyle {BoldSymbol {r}} = rho {boldsymbol {u}} _ {rho}+z {boldsymbol {u}} _ {z}}}}}}}}} v= drdt= d\u03c1dtu\u03c1+ R d\u03c6dtu\u03c6+ dzdtuz{displayStyle {BoldSymbol {v}} = {frac {{text {d}} {boldsymbol {r}}} {{text {d}} t}} = {frac {{text {d}} rho} {{text text {{text {{text {{d}} t}} = {frac {{text {text {d}} rho} {d}} t}} {BoldSymbol {u}} _ {rho}+rho {frac {{text {d}} varphi} {{text {d}} t}} {BoldSymbol {u}} _ {varphi}} +{frac {{text {d}} z} {{text {d}} t}} {boldsymbol {u}} _ {z}} . a= dvdt= d2rdt2= (d2\u03c1dt2\u2212\u03c1(d\u03c6dt)2)u\u03c1+ (2d\u03c1dtd\u03c6dt+\u03c1d2\u03c6dt2)u\u03c6+ d2zdt2uz{displayStyle {BoldSymbol {a}} = {frac {{text {d}} {boldsymbol {v}}} {{text {d}} t}} = {frac {{text {d}}^{2} {{d}} t}} = {frac {{text {text {d}}^{2} { BoldSymbol {r}}} {{text {d}} t^{2}}} = left ({frac {{text {d}}^{2} rho} {{text {d}} t^{2} }}-rho po lewej ({frac {{text {d}} varphi} {{text {d}} t}} right)^{2} prawy) {boldsymbol {u}} _ {rho}+lewy (2 {2 {2 { frac {{text {d}} rho} {{text {d}} t}} {frac {{text {d}} varphi} {{text {d}} t}}+rho {frac {{text {d {d text {d {d. }}^{2} varphi} {{text {d}} t^{2}}} right) {boldsymbol {u}} _ {varphi}+{frac {{text {d}}^{2} z} {{text {d}} t^{2}}} {BoldSymbol {u}} _ {z}} . Formu\u0142y te opieraj\u0105 si\u0119 na fakcie, \u017ce pochodna czasowa dw\u00f3ch podstawowych wektor\u00f3w jest niezerowa: du\u03c1dt= d\u03c6dtu\u03c6{displayStyle {frac {{text {d}} {boldsymbol {u}} _ {rho}} {{text {d}} t}} = {frac {{text {d}} varphi} {{text {d}} } t}} {Boldsymbol {u}} _ {varphi}} W du\u03c6dt= – d\u03c6dtu\u03c1{displayStyle {frac {{text {d}} {BoldSymbol {u}} _ {varphi}} {{text {d}} t}} =-{frac {{text {d}} varphi} {{text {d}}}} =-{frac {{text {d}} varphi} {{ }} t}} {BoldSymbol {u}} _ {rho}} . We wsp\u00f3\u0142rz\u0119dnych sferycznych [[[ modyfikator |. Modyfikator i kod ] r= R ur{DisplayStyle {BoldSymbol {r}} = r {BoldSymbol {u}} _ {r}} W v= drdt= drdtur+ R d\u03b8dtu\u03b8+ R d\u03c6dtgrzech \u2061 th u\u03c6{DisplayStyle {BoldSymbol {v}} = {frac {{text {d}} {boldsymbol {r}}} {{text {d}} t}} = {frac {{text {d}} r} {{text text {{text text} {d}} t}} {BoldSymbol {u}} _ {r}+r {frac {{text {d}} theta} {{text {d}} t}} {BoldSymbol {u}} _ {theta}}} +r {frac {{text {d}} varphi} {{text {d}} t}} sin theta {boldsymbol {u}} _ {varphi}} ; a= dvdt= d2rdt2= arur+ a\u03b8u\u03b8+ a\u03c6u\u03c6{displayStyle {BoldSymbol {a}} = {frac {{text {d}} {boldsymbol {v}}} {{text {d}} t}} = {frac {{text {d}}^{2} {{d}} t}} = {frac {{text {text {d}}^{2} { Boldsymbol {r}}} {{text {d}} t^{2}}} = a_ {r} {boldsymbol {u}} _ {r}+a_ {theta} {boldsymbol {u}} _ {theta}}}}}}}}}}}}}}}}} +a_ {varphi} {boldsymbol {u}} _ {varphi}} W z: ar= (d2rdt2\u2212r(d\u03b8dt)2+r(d\u03c6dt)2sin2\u2061\u03b8){displayStyle a_ {r} = left ({frac {{text {d}}^{2} r} {{text {d}} t^{2}}}-rleft ({frac {{text {d}}}} theta} {{text {d}} t}} right)^{2}+rleft ({frac {{text {d}} varphi} {{text {d}} t}} right)^{2} sin^ {2} Theta right)} W a\u03b8= (rd2\u03b8dt2+2drdtd\u03b8dt\u2212r(d\u03c6dt)2sin\u2061\u03b8cos\u2061\u03b8){displayStyle a_ {theta} = left (r {frac {{text {d}}^{2} theta} {{text {d}} t^{2}}}+2 {frac {{text {d}}} r} {{text {d}} t}} {frac {{text {d}} theta} {{text {d}} t}}-rleft ({frac {{text {d}} varphi} {{text {text {text {text {text ext. {d}} t}} right)^{2} sin theta cos theta right)} a\u03c6= (rd2\u03c6dt2sin\u2061\u03b8+2drdtd\u03c6dtsin\u2061\u03b8+2rd\u03c6dtd\u03b8dtcos\u2061\u03b8){displayStyle a_ {varphi} = left (r {frac {{text {d}}^{2} varphi} {{text {d}} t^{2}}} sin theta +2 {frac {{text {d. }} r} {{text {d}} t}} {frac {{text {d}} varphi} {{text {d}} t}} sin theta +2r {frac {{text {d}}} varphi} {{text {d}} t}} {frac {{text {d}} theta} {{text {d}} t}} cos theta)}}} . Albo punkt promienia wektora R w repozytorium R{DisplayStyle {Mathcal {r}}} . Albo inne repozytorium, R\u2032{DisplayStyle {Mathcal {r}}^{‘}} , kt\u00f3rego pochodzenie znajduje si\u0119 w dziale wektorowym S W R{DisplayStyle {Mathcal {r}}} . Promie\u0144 wektora punktu, okre\u015blony w R\u2032 {DisplayStyle {Mathcal {r}} ‘} jest wtedy r\u2032= r– s{DisplayStyle {BoldSymbol {r}} ‘= {BoldSymbol {r}}-{BoldSymbol {s}}}} . Pr\u0119dko\u015bci punktowe mo\u017cna zmierzy\u0107 w R{DisplayStyle {Mathcal {r}}} lub w R\u2032 {DisplayStyle {Mathcal {r}} ‘} . S\u0105 one odnotowane z indeksem R{DisplayStyle {Mathcal {r}}} Lub R\u2032 {DisplayStyle {Mathcal {r}} ‘} , a tak\u017ce przyspieszenia. Niekt\u00f3re si\u0142y [[[ modyfikator |. Modyfikator i kod ] Podstawowa zasada dynamiki [[[ modyfikator |. Modyfikator i kod ] Wektor ilo\u015bci ruchu:p=mv{DisplayStyle {BoldSymbol {p}} = m {Boldsymbol {v}}} (og\u00f3lnie) Podstawowa zasada dynamiki:dpdt=\u2211F+fie+fic{displayStyle {frac {{text {d}} {boldsymbol {p}}} {{text {d}} t}} = sum {boldsymbol {f}};+{BoldSymbol {f}} _ {rm {i_ {i_ e}}}+{BoldSymbol {f}} _ {rm {i_ {c}}}} Zasada wzajemnych dzia\u0142a\u0144: dla dw\u00f3ch cia\u0142 A I B WFA\u2192B=\u2212FB\u2192A{DisplayStyle {BoldSymbol {f}} _ {arightarrow b} =-{BoldSymbol {f}} _ {Brightarrow a}} Energia potencjalna dla niekt\u00f3rych si\u0142 konserwatywnych [[[ modyfikator |. Modyfikator i kod ] Ka\u017cda z tych energii jest zdefiniowana w pobli\u017cu Oscylator harmoniczny (bez t\u0142umienia) [[[ modyfikator |. Modyfikator i kod ] R\u00f3wnanie r\u00f3\u017cniczkowe formy:d2udt2+\u03c902u=0{displayStyle {frac {{text {d}}^{2} u} {{text {d}} t^{2}}}+omega _ {0}^{2} u = 0} . Czysta pulsacja:\u03c902=km{DisplayStyle Omega _ {0}^{2} = {frac {k} {m}}} Czysty okres:T0=2\u03c0\u03c90{DisplayStyle t_ {0} = displayStyle {frac {2pi} {omega _ {0}}}} Rozwi\u0105zanie w formie:u(t)=Acos\u2061(\u03c90t)+Bsin\u2061(\u03c90t){DisplayStyle u (t) = acos (omega _ {0} t)+bsin (omega _ {0} t)} . Sta\u0142e A I B s\u0105 okre\u015blone przez warunki pocz\u0105tkowe. Oscylator z wsp\u00f3\u0142czynnikiem t\u0142umienia L [[[ modyfikator |. Modyfikator i kod ] R\u00f3wnanie r\u00f3\u017cniczkowe formy:d2udt2+2\u03bbdudt+\u03c902u=0{displayStyle {frac {{text {d}}^{2} u} {{text {d}} t^{2}}}+2Lambda {frac {{text {d}} u} {{text {d}} } t}}+omega _ {0}^{2} u = 0} Trzy przypadki zgodnie z warto\u015bci\u0105 dyskryminacji r\u00f3wnania charakterystycznego:\u0394=4(\u03bb2\u2212\u03c902){DisplayStyle delta = 4 (Lambda ^{2} -omega _ {0} ^{2})} W ka\u017cdym przypadku sta\u0142e A I B s\u0105 okre\u015blone przez warunki pocz\u0105tkowe.        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