Page 176 - index

ɀԛɤɤɟ ԥɫɟɪ ɟɬɟɬɿɧ ɤԛɲɬɟɪ: ɫɚɥɦɚԕ ɤԛɲɿ Ɋ ɠԥɧɟ ɫɟɪɿɩɩɟɧɿԙ ɫɟɪɩɿɦɞɿɥɿɤ
ɤԛɲɿ F c ˜ O . Ԕɚɪɚɫɬɵɪɵɥɵɩ ɨɬɵɪԑɚɧ ɟɫɟɩɬɟɝɿ, ɫɟɪɿɩɩɟɧɿԙ ԕɚɬɚԙɞɵԑɵ ɞɟɩ

ɚɬɚɥɚɬɵɧ ɤɨɷɮɮɢɰɢɟɧɬ: ɫ Ɋ 100ɇ 20ɇ / ɫɦ .
Oɫɬ 5ɫɦ

Ɍɟԙ ԥɫɟɪ ɟɬɭɲɿ ɤԛɲɬɿԙ Ox ɨɫɿɧɟ ɩɪɨɟɤɰɢɹɫɵ Fx P c ˜ Ocɬ c ˜ x

ɛɨɥɚɬɵɧɵɧ ɟɫɤɟɪɿɩ, ɠԛɤ ԕɨɡԑɚɥɵɫɵɧɵԙ ɞɢɮɮɟɪɟɧɰɢɚɥɞɵԕ ɬɟԙɞɟɭɿɧ
ԕԝɪɚɦɵɡ. əԑɧɢ:

xx

m x P c ˜ Ocɬ c ˜ x .

Ȼԝɥ ɬɟԙɞɿɤɬɟɝɿ O Ocɬ x – ɫɟɪɿɩɩɟ ɞɟɮɨɪɦɚɰɢɹɫɵɧɵԙ ɲɚɦɚɫɵ, ԧɣɬɤɟɧɿ
F c ˜ O – ɠԛɤ M ɧԛɤɬɟɫɿɧɞɟ ɬԝɪԑɚɧ ɤɟɡɞɟɝɿ ɫɟɪɩɿɦɞɿɥɿɤ ɤԛɲɿ. ɀԛɤ ɬɟɩɟ-

ɬɟԙɞɿɤɬɟ ɬԝɪԑɚɧɞɚ, ɨɧɵԙ ɫɚɥɦɚԕ ɤԛɲɿ F c ˜ Oɫɬ ɲɚɦɚɫɵɧɚ ɬɟԙ ɫɟɪɩɿɦɞɿɥɿɤ
ɤԛɲɿɦɟɧ ɬɟԙɞɟɫɬɿɪɿɥɟɞɿ. ɋɨɧɞɵԕɬɚɧ:

xx

m x c ˜ x .

ɋɨԙԑɵ ɬɟԙɞɿɤɬɿԙ ɟɤɿ ɠɚԑɵɧɞɚ m -ɝɟ ɛԧɥɿɩ, ɫ ɲɚɦɚɫɵɧ k2 ɚɪԕɵɥɵ
m

ɛɟɥɝɿɥɟɩ, ԕɨɡԑɚɥɵɫɬɵԙ ɞɢɮɮɟɪɟɧɰɢɚɥɞɵԕ ɬɟԙɞɟɭɿɧɿԙ

xx k 2 x 0

x

ɬԛɪɿɧ ɚɥɚɦɵɡ.
Ȼԝɥ ɬɟԙɞɟɭ 13-ɬɟΝɞɟɭɦɟɧ ɛɿɪɞɟɣ, ɞɟɦɟɤ ɫɟɪɿɩɩɟɝɟ ɿɥɿɧɿɩ ԕɨɣԑɚɧ ɠԛɤ,
ɛԝɪɵɲɬɵԕ ɠɢɿɥɿɝɿ k -ԑɚ ɬɟԙ ɟɪɤɿɧ ɝɚɪɦɨɧɢɤɚɥɵԕ ɬɟɪɛɟɥɿɫ ɠɚɫɚɣɞɵ.

Ȼԝɪɵɲɬɵԕ ɠɢɿɥɿɤɬɿ ɬԛɪɥɟɧɞɿɪɟɣɿɤ: k 2 ɫ c P ,m P g Ÿ k g.
m Ocɬ g Oɫɬ
Oɫɬ

Ȼɚɫɬɚɩԕɵ ɲɚɪɬɬɚɪɞɵ ɬԝɠɵɪɵɦɞɚɣɵԕ:

- ɫɭɪɟɬɬɟɧ ɤԧɪɿɧɿɩ ɬԝɪԑɚɧɞɚɣ – ɈɆ 0 x0 2 ɫɦ ,

- ɛɚɫɬɚɩԕɵ ɠɵɥɞɚɦɞɵԕɬɵԙ ɨɫɿɧɟ ɩɪɨɟɤɰɢɹɫɵ x0 v0 5 ɫɦ / ɫ .

Ⱦɢɮɮɟɪɟɧɰɢɚɥɞɵԕ ɬɟԙɞɟɭɞɿԙ ɲɟɲɿɦɿɧ

x
x0
x x0 cos kt k sin kt

ɬԛɪɿɧɞɟ ԕɚɛɵɥɞɚɣɦɵɡ.

x

Ȼɟɥɝɿɥɿ ɲɚɦɚɥɚɪɞɵ ( x0 2ɫɦ, x 5ɫɦ / ɫ, k 141/ ɫ. ) ɬɟԙɞɟɭɝɟ ԕɨɣԑɚɧɧɚɧ

ɤɟɣɿɧ:
x 2 cos14t 0,357 sin14t .

Ȼԝɥ ɲɟɲɿɦɞɿ ɚɦɩɥɢɬɭɞɚɥɵԕ ɬԛɪɝɟ ɤɟɥɬɿɪɟɣɿɤ, ɨɥ ԛɲɿɧ 17- ɠΩɧɟ 18-
ɮɨɪɦɭɥɚɥɚɪɞɵ ɩɚɣɞɚɥɚɧɵɩ ɚ ɠԥɧɟ D ɲɚɦɚɥɚɪɵɧ ɬɚɛɚɦɵɡ: ɚ 2,03 ɫɦ ,

D 1,398.ɪɚɞ. Ɍɚɛɵɥԑɚɧ ɲɚɦɚɥɚɪɞɵ 16-ɮɨɪɦɭɥɚΕɚ ԕɨɹɦɵɡ. ɋɨɧɞɚ

x 2,03sin(14t 1,398) ɫɦ .

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