. () .
, ( ) ( , , ) . 3.1 .
3.1
, | |||
0,18-0,27 0,36-0,57 0,46-0,74 0,56-0,91 0,66-1,09 0,76-1,26 | 0,22-0,35 0,39-0,61 0,47-0,77 0,56-0,93 0,64-1,09 0,73-1,25 | 0,26-0,42 0,61-0,93 0,81-1,22 1,01-1,51 1,21-1,81 1,41-2,10 |
, .
: , , . , . , , .
, 9 , , , . - . 75 50 .
, . .
3.1. = 0,02cos (πt+π/ 2 ) . , , , , .
.
= cos (ωt+φ),
, ;
ω , /;
t , ;
φ , .
=2π/ω.
: 0,02 , π/ 2, 2 .
, .
|
|
υ=- 0,02 π sin (πt+π/ 2 )
a=- 0,02 π2 cos (πt+π/ 2 ).
, ,
υmax= 0,02 π /
amax= 0,02 π2 /2.
0,02cos (πt+π/ 2 )=0.
, , , 0, 1, 2, 3, 4 .
: = 0,02 , φ=π/2, = 2 , υmax= 0,0628 /, amax= 0,197 /2,
t= 0, 1, 2, 3, 4, , .
3.2 3.1
, | |
= 0,2cos (πt+π) | |
= cos (πt+π/ 4 ) | |
= 2cos (πt+π/ 3 ) | |
= 0,04cos ( 2 πt+π/ 6 ) | |
= 0,8cos (5πt) | |
= cos ( 2 πt) | |
= 0,25cos ( 4 πt+π/ 2 ) | |
= 0,5cos ( 5 πt+π/ 4 ) | |
= cos (πt+π/ 2 ) | |
= 0,1cos (πt) |
3.2. 10 = 0,1cos ( 4 πt+π/ 4 ) . .
.
= cos (ωt+φ),
, .
υ=- 0,4πsin ( 4 πt+π/ 4 )
a=- 1,6 π2 cos ( 4 πt+π/ 4 ).
υmax= 0,4 π /
amax= 1,6 π2 /2.
Fmax=mamax.
Ekmax=mυ2max/ 2.
Fmax= 0,158 , Ekmax= 7,89 .
: Fmax= 0,158 , Ekmax= 7,89 .
3.3 3.2
, | , | |
= 0,2cos (πt+π) | ||
= cos (t+π/ 4 ) | ||
=2 cos (t+π/ 3 ) | ||
= 0,04cos ( 2 πt+π/ 6 ) | ||
= 0,8cos ( 5 πt) | ||
= cos ( 2 πt) | ||
= 0,25cos ( 4 πt+π/ 2 ) | ||
= 0,5cos ( 5 πt+π/ 4 ) | ||
= cos (t+π/ 2 ) | ||
= 0,1cos (πt) |
3.3. 20 = 0,1cos ( 4 πt+π/ 4 ) . .
.
= cos (ωt+φ).
.
.
|
|
.
.
15,8 .
: =15,8 .
3.4 3.3
, | , | |
= 0,2cos (πt+π) | ||
= cos (t+π/ 4 ) | ||
= 2cos (t+π/ 3 ) | ||
= 0,04cos ( 2 πt+π/ 6 ) | ||
= 0,8cos ( 5 πt) | ||
= cos ( 2 πt) | ||
= 0,25cos ( 4 πt+π/ 2 ) | ||
= 0,5cos ( 5 πt+π/ 4 ) | ||
= cos (t+π/ 2 ) | ||
= 0,1cos (πt) |
3.4. 5 π/ 12 / . -12 , 0,15 . .
. = 0,05cos (πt/ 12 ) .
F=-kx=-Ak cos ωt,
k , /.
.
,
.
.
4 .
: t= 4 .
3.5 3.4
, | , / | , | , | |
π/ 2 | -5 | 0,15 | ||
π/ 3 | -10 | |||
π/ 4 | -15 | 0,5 | ||
π/ 6 | -20 | 0,25 | ||
π/ 3 | -10 | 0,75 | ||
π/ 2 | -20 | 0,2 | ||
π/ 4 | -25 | 0,4 | ||
π/ 6 | -5 | 0,5 | ||
π/ 12 | -12 | |||
π/ 2 | -10 | 0,5 |
3.5. k =900 / =4 , , . m =10 , υ =600 / , , . , .
. υ -
mυo=(M+m) υ,
,
.
.
: =0,1 .
3.6 3.5
, / | , | , | ,/ | |
3.6. , x1= 3cos2 πt, x2= 3cos ( 2 πt+π/ 4 ) . . .
.
= cos (ωt+φ).
, 2 π /, 3 , φ1 =0, φ2=π/ 4.
,
Δφ = φ2-φ1 . 5,54 .
|
|
.
π/ 8.
= 5,54cos ( 2 πt+π/ 8 ) .
3.1.
3.1
3.7 3.6
, | , | |
cos t | 0,01cos (t+π/ 2 ) | |
2cos πt | 0,02cos (πt+π/ 3 ) | |
3cos πt | 0,03cos (πt+π/ 3 ) | |
4cos2 πt | 0,04cos ( 2 πt+π/ 4 ) | |
5cos t | 0,05cos (t+π) | |
6cos t | 0,06cos t | |
7cos πt | 0,07cos (πt+π/ 4 ) | |
8cos πt | 0,08cos (πt+π/ 3 ) | |
9 cos2 πt | 0,09cos ( 2 πt+π/ 6 ) | |
cos t | 0,01cos (t+π/ 6 ) |
3.7. , , = cos t cos45 t, . .
.
,
ω1 ω2 ;
.
.
, ω1 =46 / ω2= 44 /.
,
, 3,14 .
: ω1 =46 /, ω2= 44 /, =3,14 .
3.8 3.7
, | |
= 0,5 cos t cos10 t | |
= 2 cos2 t cos20 t | |
= cos5 t cos25 t | |
= 2 cos10 t cos30 t | |
= cos10 t cos40 t | |
= cos20 t cos50 t | |
= 3 cos5 t cos55 t | |
= cos20 t cos60 t | |
= 4 cos20 t cos70 t | |
= cos30 t cos80 t |
3.8. , x= 3cos2 ωt y=4 cos ( 2 ωt+π), . .
. :
y=- 4cos2 ωt,
cos2 ωt=-y/ 4,
cos2 ωt=x/ 3,
-y/ 4 =x/ 3,
y=(- 4/3 )x.
, 3.2.
3.2
3.9 3.8
, | , | |
x= cos ωt | y= 4cos (ωt+π) | |
x= 3cos ωt | y= 6cos (ωt+π) | |
x= 2cos2 ωt | y= 8cos ( 2 ωt+π) | |
x= 5cos3 ωt | y= 10cos ( 3 ωt+π) | |
x= 10cos4 ωt | y= 10cos ( 4 ωt+π) | |
x= 8cos2 ωt | y= 24cos ( 2 ωt+π) | |
x= 12cos6 ωt | y= 36cos ( 6 ωt+π) | |
x= 15cos8 ωt | y= 5cos ( 8 ωt+π) | |
x= 20cos2 ωt | y= 4cos ( 2 ωt+π) | |
x= 5cos ωt | y= 5cos (ωt+π) |
3.9. , x=A sin (ωt+π/ 2 ), y=A sin ωt. . .
|
|
. :
=A cos ωt,
x2+y2=A2 cos 2ωt+A2 sin 2ωt,
x2+y2=A2.
, . x y, . . 3.3.
3.3
3.10 3.9
, | , | |
x=A cos (ωt- 2 π) | y=A sin ωt | |
x= 0,5 A sin (ωt+π/ 2 ) | y= 0,5 A sin ωt | |
x=A cos (ωt) | y=A sin ωt | |
x= 4 A sin (ωt+π/ 2 ) | y= 4 A sin ωt | |
x= 5 A sin ωt | y= 5 A sin (ωt+π/ 2 ) | |
x= 0,1 A sin (ωt+π/ 2 ) | y= 0,1 A sin ωt | |
x=A sin ωt | y=A cos ωt | |
x= 0,1 A sin ωt | y= 0,1 A sin(ωt+π/ 2 ) | |
x= 3 A sin ωt | y= 3 A cos ωt | |
x=A2 sin (ωt+π/ 2 ) | y=A2 sin ωt |
3.10. m =100 , , τ =1 40 % . r.
. δ
δ=r/2m.
.
,
.
τ =1
,
.
: r =8,51.10-4 /.
3.11 3.10
, | , % | ||
20 | |||
25 | |||
30 | |||
40 | |||
50 | |||
1 | |||
1,5 | |||
2 | |||
2 10 | |||
2 25 |
3.11. 0,2 , 1/6 =13. .
. δ
.
.
.
ω ω ω ,
.
4,98 .
: ν =4,98 .
3.12 3.11
, | ||
0,1 | ||
0,2 | ||
0,3 | ||
0,4 | ||
0,5 | ||
0,6 | ||
1,3 | ||
1,5 | ||
1,8 |