1. x =0, - w0 = 4-1. x 0 = 25 u0 = 100 /. x u t = 2,4 .
:
x = Acos(w0t + j0), (1)
:
(2)
. t = 0 :
0 = cosj0,
u0 = -w0sinj0,
φ0= -p/4,
.
u t = 2,4 (1) (2):
= - 29 , u = -81 /.
2. = 0,6 = 10 . , /2:
) ; ) .
, . :
= sinw0t.
t1, = /2. :
,
t1 = T / 12.
:
u1 = 100 /.
:
.
:
; u2 = 50 /.
:
3. , , : 1 = 3cos(wt + p/3) , 2 = 8sin(wt + p/3) .
.
, ,
2 = 8 cos(wt - p/6) .
1 0 φ 1 φ2 2 |
,
Dj = j2 - j1.
, = 8,5 .
, j = - 0.2 .
:
0
l lc
c
m3
=8,5cos(wt 0.2) . m2
4. l = 1 m1 = 0,4 m2 = 0,2 m3 = 0,4 . - , . - , .
(. .) ,
,
I - ; m ; l c .
|
|
,
I = (1/12) m1l 2 + m2 (l /2)2 + m3 (l /2)2 = (1/12) l 2(m 1 + 3 m 2 + 3 m 3),
I = 158 ּ 2.
m = m1 + m2 + m3 = 0,9 .
l c
, l c = 5,55 , = 11,2 .
5. m = 5 . t =50 60 % . r.
, ,
E = mA2w2/2.
A = 0 - b t,
E = E0 -2b t, (1)
t = 0.
t =50 60 % - , ,
E = 0,4 E0. (2)
(1) (2), E0 , , :
ln 2,5 = 2 bt.
b:
b = (ln 2,5)/2 t. (3)
, b = r/2m. (4)
(3) (4) r = (m ln2,5)/ t
r = 9,16×10-5 /.
6. m = 10 7 , , , , 1,6 -1. , . x =5sin(10pt - 0,75p) . : 1) - ; 2) .
= 0 - bt sinw t, (1)
- ; w0 ; b - .
j - 3p/4; , tg (-3p/4) = 1.
,
c (2)
w = 10p, b = 1,6 -1. (2), , b2 << w02, , w w0 . ,
= 7 e -1,6 t sin 10,5 w p t .
F = F0 sinw t. (3)
(4)
F0 =
= 72 .
F = 72 sin 10 p t .
7. , , F = F0 sinw t. - . ?
, (1)
(2)
, (2)
.1
,
, - 0 2 um, 0 (. 2.).
|
|
x |
0 T t |
υ 2υm |
T 2T t |
. 1 . 2
8. υ =20 /. , 1 =12 2 =15 , Δ φ = 0,75 π. λ, t = 1,2 , = 0,1 .
, , λ, , 2 π; , Δ x, ,
.
λ,
. (1)
, (1), λ = 8 .
, , ω. ω=2π/T (T = λ/υ ),
.
,
, ω υ,
(2)
= 0,1 , ω= 5 π -1, υ= 20 /c.
y, (2) t :
y1 = - 0,1 ; y2 = 7,1 .
9. , , . , , .
:
, (1)
,
.
. , ,
. (2)
. (3)
I = 0,
.
. , (2)
.
(3)
, .
R |
C |
L |
E |
10. , - , - , - . , . I UR, UL, UC , .
.
.
, - (, ), :
.
,
, .
. , . :
,
,
.
5.
5.1. .
, . , , (, - , .) - . ,
(5.1)
A - , - , - .
.
.
|
|
, (5.2)
n- .
, .
ν ,
. (5.3)
, , .
(5.4)
n - .
, (5.1), . , ( ) - . , . ∆ν, .
, , . , . τ ≈ . - . . , , . , . , , . . , .