Яблонский К3, К7, К1 вариант 27 / Д-3 вар 27 / Д3_27

3 ( 27)

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3.

# : mx = P − F − R.

* F = 2cλ, λ = (λ + ) − #

, . .

mx = P − 2

(λ +

) − 400V

mx = P − 2 λ

− 2

− 400x.

# D

F = P = 2cλ .

(1)

$

mx = −2

− 400x

mx + 400x + 2cx = 0,

(2)

$## ,

x +10x + 6.5x = 0.

" # #(1)

p2 +10 p + 6.5 = 0,

= −5 ±

= −5 ±

≈ −5 ± 4.3

p1 ≈ −9.3,

p2 ≈ −0.7 .

p1,2

25 − 6.5

18.5

* % ) % #(2)

x = C e−9.3t + C

e−0.7t .

(3)

1

2

( (1) , λ =

P

= mg =

40 ×981 » 150.92 , x

= -150.92 .

2c

2c

2 ×130

0

( t = 0,

x0 = -150.92,

x0

= V0 = 0.

, (3)

x0 = C1 + C2

C1 = -C2 + x0

= -C2 -150.92;

x = -9.3C1e

−9.3t

- 0.7C2e

−0.7t

0 = -9.3C1 - 0.7C2

C2 » -13.31 1.

C2 = -13.31×(- 2 -150.92) 2

» -163.18;

C1 = -150.92 - C2 = -150.92 +163.18 » 12.26