мет.указ. к.р. №3
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, 20 __ .
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3
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, 1110- -1268 – 4
, – 6 .
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1..
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3.( 3),
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5.,
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6., ,
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7.,
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9., .
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[v] = |
GM [ 3 1 2 ] [ ] [ 1 ] 1 |
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10. ,
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, . 11.
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12.
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10, 0,000347, 3,47·10-4. 13. .
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15. ,
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16.
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1.. . : . .: , 2008
2.. . .: , 2009
3.. . .:
. 2008
4.. . . . .: , 2000
5.. . . .: , 2001
6.. . . . 1-2. – ., , 2005
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7.. . , .: , 2001
8.. . . , .: , 2004
9.. . 500 . .,
, 2003
10.. , . . . .: , 2002
1.
1.1.
:
x = Acos ( 0t + ); x = A sin ( 0t + ),
x – ;– ;
=2 =2 /T – ( ) ;
- ; T – ; – .
, ;
vx= |
dx |
t = -A 0sin (w0t + ) = - A 0cos ( ot + + /2); |
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dt |
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d 2 x |
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ax= |
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dv |
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x |
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= - A |
cos ( 0t + ) = - 0 |
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dx |
dt 2 |
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m |
d 2 x |
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- kx |
d 2 x |
02 0 , 02 |
= k/m |
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2 |
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dt |
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dt 2 |
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m:
Wk =mv2/2 = mA2 02sin2 0t + )/2.
: Wn= mA2 02cos2 0t + )/2.
: W = Wk + Wn = mA2 02/2 = const
:
: 2 m
k
: T 2 |
l |
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: T 2 |
J |
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2 L , |
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mgl |
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J – ; l – ; L =J/ml – ;
g –
:
d 2 x |
2 |
dx |
02 x 0 ; x = Ae tcos ( t + ), |
dt 2 |
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dt |
x – , ;= r/2m – ;
r – ; m – ;
0 –
;= ( 02- 2)1/2- ;
Ae t – .
: A(t)/A(t +T) = e t,
A(t), A(t+T) –
, .
:
=ln A(t)/ A(t+T) = T = T/ = 1/N,
–
N – , .
:
= / = 0/2
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d 2 x |
2 |
dx |
2 x F cos t |
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dt 2 |
dt |
0 |
0 |
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x= Acos ( t - ), |
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x – ; |
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F=F0cos t – , ; |
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A |
F0 |
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A = F0/ m [( 02 |
- 2) + 4 2]1/2; |
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m ( 02 2 ) 4 2 |
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=arctg 2 /(v02 2) |
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: P |
02 2 2 ; |
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AP |
F0 |
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2m 02 2 |
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1.2.
, T :
= vT = v/ ; v = ,
v ( )
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: x(t) = Acos ( t – kx + 0)
(t) – ;
A – ;
– ( ) ;
k= 2 =2 /vT = /v – ;
– ; v ;
T – ;
0 –
d: = d/
:
max= ± 2 m; min= ± (2m+1) mdvax = ±m ; dmin= ± (2m+1) /2,
m = 0, 1, 2.
v u:
v= /k; u =d /dk; u = v - dv/d
:
x(t) = 2A(cos 2 x / )cos t = 2Acoskx cos t.
n :
xn = + m /2; xy = + (m +1/2) /2, m=0, 1, 2.
1.3.
– ,
, ,
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R=0, :
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W |
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Q 2 |
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LI |
2 |
const , |
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Q 2 |
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CU 2 |
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2C |
2 |
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W |
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QU |
– , |
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2C |
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WM |
LI |
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d 2Q |
02Q 0 |
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dt 2 |
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: Q Q0 cos( 0t ) . |
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0 = |
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LC |
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( ): T 2 2 LC
0
d 2 Q |
2 |
dQ |
02 Q 0 , |
dt 2 |
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dt |
R -
2L
1
0 = -
LC
: Q Q0 cos( t ) .
Q Q0
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R 2 |
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LC |
4L2 |
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: T |
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LC 4L2 |
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1.5
d 2 Q |
2 |
dQ |
02 Q EM cos t , |
dt 2 |
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dt |
R –
2L
1
0 = –
LC
: QM |
EM |
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L ( 02 2 ) 4 2 2 |
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R 2 |
: Pe3 0 |
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LC |
2L2 |
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: I I 0 cos( t )
: PE 3 0 1
LC
1.6.
RL L
: RC 1
C
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X R |
L |
R L |
1 |
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: Z |
R |
2 |
(RL RC ) |
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1 2 |
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( ) : I I M |
U U M |
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2 |
2 |
– ,
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: k U1 N1 ,
U 2 N 2
U1 ,U 2 –
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N1 , N 2 –
k 1 –
k 1 –
2 – .
2.1.
:
:
: n=
: ,
n – , s –
: = L2 – L1
:=
2.2. .
: = ±m (m=1, 2, 3…)
: =±(2m+1) |
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(m=1, 2, 3…) |
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:
=2d +
d – ¸ i –
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(m=1, 2, 3…)
d = a +b – , – ¸ m –
: (m= 0, N, 2N…)
N –
:
:
:
,
–
: ,
n21 –
: d,
=[ ]Cd
– , d – , –
2.3.
:
:
– :
,– – , –
: ,
b –
:
: =
: = A +
: =
:
3.
, . 3.1
: = m/M; = V/VM,
m – ; M – ; V – , VM – .
: m0= M/NA; m0 = /n,
– ,
NA= 6,023·1023 -1 – ;
– ; n0 – , : n0 = N/V; n = /m0; n = NA/M.
: N = m/m0 = m Na/M.
T,K = t°C +273,15; t°C = T,K – 273,15°
3.2. .
( –
):
; pV = RT -
: pV = mRT/M; pV = RT -
V – ; M – ; m – ;
= m/M – ; R –
( ): pV/T =const; p1V1/T1 = p2V2/T2
p – ; V – ; T –
– ( ):
pV = const; p1V1= p2V2 T=const, m = const
( ):
V =V0(1 + t) V/T =const; V1/V2= T1/T2 p =const, m =const
( ):
= 0(1 + t) p/T =const; p1/p2 = T1/T2 V =const, m =const,
t ,
V0, p0 – 00 ,
=1/273 -1,
p, V, T ,
n
n : p = pi ,
i 1
pi – i-
:
0 = 00 =273 , 0 =1 =1,013·105
V =22,4 -1 = 2,24·10-2 3 -1