- ÃÀËÓÀ ÃÐÓÏÏÀ
- ÃÀËÓÀ ÒÅÎÐÈß
- ÃÀÌÌÀ-ÔÓÍÊÖÈß
- ÃÀÐÌÎÍÈÊÀ
-
ÃÀÐÌÎÍÈÊÀ
ÃÀÐÌÎÍÈÊÀ — ôóíêöèÿ âèäà
. Ã. åñòü ïåðèîäè÷åñêàÿ ôóíêöèÿ ñ ïåðèîäîì
. Êîëåáàòåëüíîå äâèæåíèå, ñîâåðøàåìîå ïî ôîðìóëå
(ïåðåìåííàÿ
— âðåìÿ), íàçûâàåòñÿ ïðîñòûì ãàðìîíè÷åñêèì êîëåáàíèåì; ïðè ýòîì ÷èñëî
íàçûâàåòñÿ àìïëèòóäîé êîëåáàíèÿ,
— êðóãîâîé ÷àñòîòîé (êðóãîâîé ñêîðîñòüþ),
— íà÷àëüíîé ôàçîé êîëåáàíèÿ. Ôóíêöèè
;
,... íàçûâàþòñÿ ñîîòâåòñòâåííî âòîðîé, òðåòüåé è ò.ä. âûñøèìè Ã. îòíîñèòåëüíî îñíîâíîé Ã.
.
×èñëî
íàçûâàåòñÿ ÷àñòîòîé êîëåáàíèÿ. Åñëè
— ÷àñòîòà ïåðâîé, èëè îñíîâíîé, Ã., òî ÷àñòîòû âûñøèõ Ã. ðàâíû
(âòîðàÿ Ã.),
(òðåòüÿ Ã.) è ò. ä.
×àñòî ïåðèîäè÷åñêóþ ôóíêöèþ
ìîæíî àíàëèòè÷åñêè ïðåäñòàâèòü â âèäå ñóììû Ã. (ñì. Ãàðìîíè÷åñêèé àíàëèç):
,
ãäå
— ïîñòîÿííàÿ ñðåäíÿÿ âåëè÷èíà ôóíêöèè
, îêîëî êîòîðîé ïðîèñõîäèò êîëåáàíèå,
— àìïëèòóäà è ôàçà ïåðâîé (îñíîâíîé) Ã.,
— àìïëèòóäà è ôàçà âòîðîé Ã. è ò. ä.
Îáùèé âèä ïðîñòîé Ã. ñ ÷àñòîòîé
ìîæíî çàïèñàòü è â âèäå
, ãäå
è
— äåéñòâèòåëüíûå ÷èñëà:
.
Ãðàôèê Ã. ïîëó÷àåòñÿ èç ãðàôèêà
ïóòåì ïîñëåäîâàòåëüíîãî ïîñòðîåíèÿ è ïðåîáðàçîâàíèÿ ãðàôèêîâ ôóíêöèé:
,
,
,
;
ãðàôèê
ðàñòÿãèâàþò â íàïðàâëåíèè îñè
â
ðàç, çàòåì ïîëó÷åííûé ãðàôèê ñæèìàþò ïî îñè
â
ðàç è, íàêîíåö, ïîëó÷åííûé ãðàôèê ïåðåíîñÿò (ñäâèãàþò) â íàïðàâëåíèè îñè
íà
åäèíèöû äëèíû.
Îäíèì èç ãëàâíûõ ñâîéñòâ Ã.
ÿâëÿåòñÿ òî îáñòîÿòåëüñòâî, ÷òî Ã. óäîâëåòâîðÿåò äèôôåðåíöèàëüíîìó óðàâíåíèþ
,
, êîòîðîå îïèñûâàåò êîëåáàíèå ìàòåðèàëüíîé òî÷êè ìàññû
îêîëî òî÷êè
ïðè óñëîâèè, ÷òî ñèëà, äåéñòâóþùàÿ íà òî÷êó, ïðîïîðöèîíàëüíà îòêëîíåíèþ
îò òî÷êè ðàâíîâåñèÿ
(è íàïðàâëåíà â ñòîðîíó òî÷êè
).
Ñì. òàêæå: Ñèíóñîèäà.
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