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§4. Ɋɟɡɨɧɚɧɫ ԕԝɛɵɥɵɫɵ
38-ɬɟΝɞɟɭɞɿΝ ɞɟɪɛɟɫ ɲɟɲɿɦɿɧ

x2 C ˜ t ˜ cos(kt G ) , (51)
ɬԛɪɿɧɞɟ ɿɡɞɟɣɦɿɡ.

Ȼԝɥ ɬɟԙɞɟɭɞɟɝɿ C – ɬԝɪɚԕɬɵ ɲɚɦɚ, ɨɧɵ ɚɧɵԕɬɚɭ ɤɟɪɟɤ.

xx 2Ck sin(kt G ) 2Ck 2 cos(kt G ) .

Ɍɟԙɞɟɭɞɿԙ (51) ɟɤɿɧɲɿ ɬɭɵɧɞɵɫɵ: x 2

ȿɧɞɿ 38-ɬɟΝɞɟɭɝɟ x2 -ɧɿ ɠԥɧɟ ɨɧɵԙ ɟɤɿɧɲɿ ɬɭɵɧɞɵɫɵɧ ԕɨɹɦɵɡ, ɫɨɧɞɚ:
2Ck sin(kt G ) h sin(kt G ) .

Ɍɟԙɞɿɤɬɿԙ ɟɤɿ ɠɚԑɵɧɞɚԑɵ sin(kt G ) ɲɚɦɚɫɵɧɵԙ ɤɨɷɮɮɢɰɢɟɧɬɬɟɪɿ ɛɿɪ-

ɛɿɪɿɦɟɧ ɬɟԙ ɛɨɥɭ ɤɟɪɟɤ, ɫɨɧɞɵԕɬɚɧ: 2Ck h . Ɉɫɵԑɚɧ ɛɚɣɥɚɧɵɫɬɵ

C h ɠԥɧɟ x2 ht cos(kt G ) . (52)
2k 2k

Ȼԝɥ ɮɨɪɦɭɥɚɧɵ, cos(kt G ) sin(kt G S ) ɬɟԙɞɿɝɿɧ ɟɫɤɟɪɿɩ, ɤɟɥɟɫɿ
2

ɬԛɪɞɟ ɠɚɡɚɦɵɡ:

x2 ht sin(kt G S ) . (53)
2k 2

ȿɧɞɿ 38-ɞɢɮɮɟɪɟɧɰɢɚɥɞɵΙ ɬɟԙɞɟɭɞɿԙ ɬɨɥɵԕ ɲɟɲɿɦɿɧ ɤɟɥɬɿɪɟɣɿɤ:

x a ˜ sin(kt D) ht (kt G S ) . (54)
2k 2

Ɋɟɡɨɧɚɧɫ ɤɟɡɿɧɞɟɝɿ ɬɚɡɚ ɚɦɚɥɫɵɡ ɬɟɪɛɟɥɿɫɬɿ ԕɚɪɚɫɬɵɪɚɣɵԕ. Ɋɟɡɨɧɚɧɫ

ɤɟɡɿɧɞɟ, ɚɦɚɥɫɵɡ ɬɟɪɛɟɥɿɫ ɚɭɵɬԕɵɲɬɵԕ ɤԛɲɿɧɟɧ ɮɚɡɚɫɵ ɛɨɣɵɧɲɚ S
2

ɲɚɦɚɫɵɧɚ ԕɚɥɵɩ ԕɨɹɬɵɧɵɧ 53-ɮɨɪɦɭɥɚɞɚɧ ɤԧɪɭɝɟ ɛɨɥɚɞɵ. ɋɢɧɭɫɬɵԙ
ԧɡɝɟɪɦɟɥɿ ɤɨɷɮɮɢɰɢɟɧɬɿɧɿԙ ɦɨɞɭɥɿɧɿԙ ɲɚɦɚɫɵ – ɪɟɡɨɧɚɧɫ ɤɟɡɿɧɞɟɝɿ ɚɦɚɥɫɵɡ
ɬɟɪɛɟɥɿɫɬɿԙ ɚɦɩɥɢɬɭɞɚɫɵ ɛɨɥɵɩ ɫɚɧɚɥɚɞɵ, ɹԑɧɢ

B ɪɟɡ ht . (55)
2kɪ

Ʉɟɥɬɿɪɿɥɝɟɧ ɮɨɪɦɭɥɚ (55) ɛɨɣɵɧɲɚ, ɪɟɡɨɧɚɧɫ ɤɟɡɿɧɞɟ ɚɦɩɥɢɬɭɞɚ ɭɚԕɵɬԕɚ
ɩɪɨɩɨɪɰɢɨɧɚɥ ɠԥɧɟ ɲɟɤɫɿɡ ԧɫɟɞɿ, ɛɿɪɚԕ ɬɟɪɛɟɥɿɫ ɤɟɡɿɧɞɟ, ԥɪ ɭɚԕɵɬɬɚ ɞɚ,
ɤɟɞɟɪɝɿ ɬɭɵɧɞɚɣɬɵɧ ɛɨɥԑɚɧɞɵԕɬɚɧ, ɚɦɩɥɢɬɭɞɚ ԛɥɤɟɧ ɛɨɥԑɚɧɵɦɟɧ, ɨɥ ɲɟɤɫɿɡ
ԧɫɩɟɣɞɿ. Ⱥɦɩɥɢɬɭɞɚɧɵԙ ɪɟɡɨɧɚɧɫ ɤɟɡɿɧɞɟ ԕɚɪԕɵɧɞɚɩ ԧɫɭɿ ɤԧɩɬɟɝɟɧ
ԕɢɵɧɞɵԕɬɚɪ ɬɭɞɵɪɚɞɵ.
Ɇɵɫɚɥɵ, ԑɢɦɚɪɚɬɬɚɪɞɵԙ, ɤԧɩɿɪɥɟɪɞɿԙ, ɦɨɬɨɪɞɵԙ, ɦɚɲɢɧɚɥɚɪɞɵԙ ɠԥɧɟ
ɬɚԑɵ ɛɚɫԕɚɥɚɪɞɵԙ ԕɢɪɚɭɵɧɚ (ɿɫɬɟɧ ɲɵԑɭɵɧɚ) ԥɤɟɩ ɫɨԑɚɞɵ. ɋɨɧɞɵԕɬɚɧ
ɪɟɡɨɧɚɧɫ ԕԝɛɵɥɵɫɵɧɚ ɬɟɯɧɢɤɚɞɚ ɤԧɩ ɤԧԙɿɥ ɛԧɥɭ ɤɟɪɟɤɬɿɝɿ ɬɭɵɧɞɚɣɞɵ.
ȿɪɿɤɫɿɡ ɬɟɪɛɟɥɿɫɬɿԙ ɪɟɡɨɧɚɧɫ ɤɟɡɿɧɞɟɝɿ ɝɪɚɮɢɝɿɧ ɬԝɪԑɵɡɚɣɵԕ (13-ɫɭɪɟɬ).

Ⱥɥɞɵɦɟɧ, ɟɤɿ ɲɟɤɬɟɭ ɬԛɡɭɥɟɪɿɧ ɠԛɪɝɿɡɟɦɿɡ, ɨɥɚɪɞɵԙ ɬɟԙɞɟɭɥɟɪɿ X1 ht
2k

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