Page 173 - index

xx (12)

m x Fx c ˜ x

Ȼɨɥɵɩ ɠɚɡɵɥɚɞɵ.
Ɍɟԙɞɿɤɬɿԙ ɟɤɿ ɠɚԑɵɧ m -ɝɟ ɛԧɥɿɩ, ɤɟɥɟɫɿ ɛɟɥɝɿɥɟɭɞɿ ԕɚɛɵɥɞɚɣɦɵɡ:

c k2.
m
Ɉɫɵɞɚɧ ɤɟɣɿɧ ɤɟɥɟɫɿ ɞɢɮɮɟɪɟɧɰɢɚɥɞɵԕ ɬɟԙɞɟɭɞɿ ɚɥɚɦɵɡ:

xx k 2 x 0. (13)
ɬɟɪɛɟɥɿɫɿɧΝ
x

Ɉɫɵ ɬɟԙɞɟɭ – ɧΟɤɬɟɧɿΝ ɟɪɤɿɧ ɝɚɪɦɨɧɢɤɚɥɵΙ
ɞɢɮɮɟɪɟɧɰɢɚɥɞɵΙ ɬɟΝɞɟɭɿ ɛɨɥɵɩ ɬɚɛɵɥɚɞɵ.
ȿɧɞɿ, ԕɨɡԑɚɥɵɫɬɵԙ ɛɚɫɬɚɩԕɵ ɲɚɪɬɬɚɪɵɧ ɬԝɠɵɪɵɦɞɚɣɵԕ:

- ɚɥԑɚɲԕɵ ɫԥɬɬɟ ɧԛɤɬɟ M 0 ɨɪɧɵɧɞɚ ɛɨɥɫɵɧ,

xx

- ɠɵɥɞɚɦɞɵԑɵɧɵԙ Ɉx ɨɫɿɧɟ ɩɪɨɟɤɰɢɹɫɵ x0 , ɹԑɧɢ t t0 , x x0 ɠԥɧɟ x x0 .

13-ɬɟΝɞɟɭ xx k 2x 0 ) ɤɨɷɮɮɢɰɢɟɧɬɿ ɬԝɪɚԕɬɵ, ɛɿɪɬɟɤɬɿ ɫɵɡɵԕɬɵԕ ɬɟԙɞɟɭ

( x

ɛɨɥԑɚɧɞɵԕɬɚɧ, ɨɧɵ ɲɟɲɭ ԛɲɿɧ ɫɢɩɚɬɬɚɦɚɥɵԕ (ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɥɵԕ) ɬɟԙɞɟɭ

ԕԝɪɵɩ, ɨɧɵԙ ɬԛɛɿɪɥɟɪɿɧ ɬɚɛɭ ɤɟɪɟɤ. Ɉɥ ɬɟԙɞɟɭ: r 2 k 2 0 , ɚɥ ɬԛɛɿɪɥɟɪɿ

r1 ki ɠԥɧɟ r2 ki , ɛԝɥ ɬɟԙɞɿɤɬɟɪɞɟɝɿ i 1 . ɋɨɧɵɦɟɧ, 13-ɬɟΝɞɟɭɞɿΝ
ɲɟɲɭɿ:

x C1 cos kt C2 sin kt . (14)

ɂɧɬɟɝɪɚɥɞɚɭɞɵԙ ɬԝɪɚԕɬɵɥɚɪɵ ɛɚɫɬɚɩԕɵ ɲɚɪɬɬɚɪɞɚɧ ɬɚɛɵɥɚɞɵ.

- Ȼɿɪɿɧɲɿ ɲɚɪɬ ɛɨɣɵɧɲɚ: ɟɝɟɪ t t0 ɛɨɥɫɚ, ɨɧɞɚ x x0 . Ɉɫɵ ɲɚɪɬɬɵ 14-

ɬɟΝɞɟɭɝɟ ԕɨɹɦɵɡ, ɫɨɧɞɚ:

x0 C1 cos 0 C2 sin 0 Ÿ x0 C1 .

xx

- ȿɤɿɧɲɿ ɲɚɪɬ ɛɨɣɵɧɲɚ: ɟɝɟɪ t t0 ɛɨɥɫɚ, ɨɧɞɚ x x0 . Ȼԝɥ ɲɚɪɬɬɵ

ԕɨɥɞɚɧɭ ԛɲɿɧ, ɚɥɞɵɦɟɧ 14-ɬɟΝɞɟɭɞɿ ɞɢɮɮɟɪɟɧɰɢɚɥɞɚɣɦɵɡ, ɹԑɧɢ

xx x0 .
k
x x0 C1k sin 0 C2k cos 0 Ÿ C2

ɋɨɧɵɦɟɧ, ɧԛɤɬɟ ԕɨɡԑɚɥɵɫɵɧɵԙ ɬɟԙɞɟɭɿɧ ɚɥɞɵԕ. Ɉɥ:

x x0 ˜ cos kt x0 ˜ sin kt . (15)
k

ɇԛɤɬɟ ԕɨɡԑɚɥɵɫɵɧɵԙ ɫɢɩɚɬɬɚɦɚɥɚɪɵɧ ɚɣԕɵɧ ɤԧɪɫɟɬɭ ԛɲɿɧ 14-ɮɨɪɦɭɥɚɧɵ
ɛɚɫԕɚɲɚ ԧɪɧɟɤɬɟɣɿɤ. Ɉɥ ԛɲɿɧ, ɢɧɬɟɝɪɚɥɞɚɭɞɵԙ ɬԝɪɚԕɬɵɥɚɪɵɧ

a ˜ sin D C1 , a ˜ cosD C2

ɬԝɪɚԕɬɵɥɚɪɦɟɧ ɚɥɦɚɫɬɵɪɚɣɵԕ.
Ɉɫɵ ɲɚɦɚɥɚɪɞɵ 14-ɮɨɪɦɭɥɚΕɚ ԕɨɣɫɚԕ:

x a ˜ sin(kt D ) . (16)

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