[1.1] r 1 =10e j(ωt+π/4), r 2 =5e j(ωt+π/3), r 3 =3e j(ωt+π/6) ~r = ~r 1 + ~r 2 + ~r 3 = re j(ωt+φ) =(10e π 4 j +5e π 3 j +3e π 6 j )e jωt

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やすはるにばし
4 years ago
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1 3.4.7 [.] =e j(t+/4), =5e j(t+/3), 3 =3e j(t+/6) ~ = ~ + ~ + ~ 3 = e j(t+φ) =(e 4 j +5e 3 j +3e 6 j )e jt = e jφ e jt cos φ =cos 4 +5cos 3 +3cos 6 =.69 sin φ =sin 4 +5sin 3 +3sin 6 =.9 = =7.74 [.] φ =tan (.9/.69) = [.85 ad] x =4cos(t/6+/4),x =5cos(t/5+/3) ~x = ~x + ~x =4cos( 6 t + 4 )+5cos( 5 t + 3 ) (.5) ½ ³ ~x = cos 6 + t ³ ¾ µ t 3 + Ψ = cos Ψ (.4) = cos n³ 6 t o ³ = cos 3 3 t + [.3] Ψ = 4 5 µ 4+5 tan t 6 = µ t 4 9 tan 6 + 4

2 θ : f(θ) = A θ θ 3 : f(θ) =A A θ 3 θ : f(θ) =A θ 4A a n = b n = T Z T f(t)sinntdt = Z A t sin ntdt + Z 3 + A sin ntdt Z 3 µ A Z 3 A t sin ntdt t 4A sin ntdt Z t sin ntdt = t cos nt + Z n n cos ntdt = t cos nt + [sin nt] n n b n = 4A µ sin n n 3n sin b = 8A,b =,b 3 = 8A 9,b 4 =,b 5 = 8A 5,... a = T Z T f(t)dt = Z A tdt + Z 3 Adt Z 3 A tdt + Z 3 µ A t 4A dt = f(t) = 8A sin t (/3 )sin3t +(/5 )sin5t...

3 [.4] θ : f(θ) = A θ θ : f(θ) = A θ A a n = a b n = A Z = A + A t sin ntdt + A Z n o ½ n cos n + A t sin ntdt A cos n + n Z sin ntdt ¾ cos n n ½ ¾ cos n cos n = A cos n = A n n n n ( )n f(t) = A [sin t (/) sin t +(/3) sin 3t... ] [.5] θ : f(θ) = A θ a n = Z A t cos ntdt = A = A ( t sin nt n + cos nt n ½ + ¾ cos n = n n ) a = Z A tdt = At 4 3 = A 8 µ 4 = A

4 b n = Z A t sin ntdt = A = A A ( t cos nt n = A ½ + ¾ cos n n sin nt n = A n f(t) = a + X b n sin nt n= µsin t + sin t + 3 sin 3t... ) 4

5 [.] f = k m =3.Hz 5g f = k m +5 =.5Hz m +5 m = 3..5 m =7.83kg k =365.3N/m =3.7kN/m [.] ρ d 4 x g mẍ + 4 d ρgx = n = d ρg 4m ad/s [.3] mb θ = k(aθ) a mb θ + ka θ = n = a b k m ad/s 5

6 [.4] m x y mẍ + k (x y) = ³ a k ya = k (x y)l l k a y = k l (x y) y = k l k a + k l x x µ k l mẍ + k x = k a + k l mẍ + k k a k a + k l x = s k k a n = (k a + k l )m ad/s [.5] α x cos α -5 mẍ +(kx cos α)cosα = mẍ + kx cos α = k n = m cos α ad/s [.6] 6

7 ml θ = k(aθ) a +(mg sin θ) l ml θ + ka θ mgθl = ka mgl n = ad/s ml [.7] µ a x a mg µ a + x a mg mẍ = µ a x + x mg µa a a mg ẍ + µg a x = µg n = ad/s () a [.8] m e e sin t (M + m + m e )ẍ + kx = m e e sin t x = C sin t (M + m + m e )C sin t + kc sin t = m e e sin t C = m e e k (M + m + m e ) x = m e e sin t k (M + m + m e ) m e e 4 ẍ = sin t k (M + m + m e ) m e e 4 k (M + m + m e ) g (9) 9.8 () 7

8 =36.4ad/s [.9] m =kg,c =Ns/m,k =kn/m ζ = δ = c mk = =.58 ζ ζ = =.5 [.] T = n = km n T = n mẍ + csẋ + kx = ẍ +ζ n ẋ + nx = ζ T T = n = ζ ζ = n = cs mk c = mk(n )/ns(n s/m) [.] θ ml θ + cb θ + ka θ = n = a l km ζ = cb al mk d = n ζ = a km c b 4 l 4mkl a = 4mkl a ml c b 4 8

9 [.] mẍ + cẋ + kx = f sin t k = n m =() = 98.7kN/m X = F /k ζ ζ = F kx =.68 c =ζ mk = =47.3Ns/m [.3] mẍ + c(ẋ ẏ)+kx = y = Y sin t mẍ + cẋ + kx = cy cos t ẍ +ζ n ẋ + x = ζ n Y cos t x = C cos t + D sin t cos t, sin t C(n )+Dζ n = ζ n Y Cζ n + D(n ) = D = C = (ζ n ) Y (n ) +(ζ n ) ζ n (n )Y (n ) +(ζ n ) x = ζ n Y ( n ) +(ζ n ) sin(tφ) [.4] µ φ =tan ζn n 9

10 / ζ ζ = log ζ (log ) = () +(log) =.539 ζ =.73 c = ζ mk =.73 = 4.6Ns/m k n = m = =3.6ad/s =ad/s F =N (.7) X = = X st ( (/n ) ) +(ζ(/ n )) / =.6m =.cm ( (/3.6) ) +(.73(/3.6)) [.5] K = Gd4,G: 3l J θ + c θ + Kθ = T sin t K Gd n = J = 4 c, ζ = 3l JK = c Gd 4 /3l (.7) Θ = T /K ( (/n ) ) +(ζ(/ n )) T /K = T /(Jn) [.6] (.93)

11 .5 f(t) = F F µsin t + sin t + 3 sin 3t... F x = F = Xst k f i = F sin it i x i = (X st /i)sin(it φ i ) { (i/n ) } + {ζ(i/ n )}, φ i =tan ζ(i/ n ) (i/ n ) [.7] x(t) = X st X i x i k n = m = =4.4ad/s 5 ζ = c mk = 5 =.4 F = kn = = 6.83ad/s = n (.9) F T = F +{ζ(/n )} { (/n ) } + {ζ(/ n )} = [.8] =8536.4N =8.54kN mẍ + k(x Y sin t) = ẍ + nx = ny sin t (.6) x = v = Y x = (/ n ) [sin t (/ n)sin n t] q Y =5 m, =4 =.566ad/s, n = t =8.65ad/s 3 x =5.6(sin 8.65t.65 sin.566t)cm

12 [.9] ẍ + ẋ + x = e t, t = >x=, ẋ = (4, ) s X(s) sx() ẋ() + sx(s) x() + X(S) = X(s) = (s + s +)X(s) = (s )(s + s +) + s s s + s + µ µ x(t) = L + L s s + s + s + s + = 3 L s s + 3 (s + ) + 3 (s + 4 ) L (s + 4 ) Ã =! e t e t 3 cos 3 t t 3 e sin t + e t 3 sin 3 t Ã = 3 et e t 3 cos t! 3 3sin t [.] () () s +3 s +s +5 = (s +)+ (s +) +4 = e t (cos t +sint) s + (s )(s +s +) a s + bs + c s +s + = a(s +s +)+(bs + c)(s ) (s )(s +s +) a = 3 5, b = 3 5, c = s 3(s +)+ 5 (s +) + = 3 5 et 3 5 cos t 5 sin t

() (, y) E(, y) () E(, y) (3) q ( ) () E(, y) = k q q (, y) () E(, y) = k r r (3).3 [.7 ] f y = f y () f(, y) = y () f(, y) = tan y y ( ) () f y = f y

() (, y) E(, y) () E(, y) (3) q ( ) () E(, y) = k q q (, y) () E(, y) = k r r (3).3 [.7 ] f y = f y () f(, y) = y () f(, y) = tan y y ( ) () f y = f y 5. [. ] z = f(, y) () z = 3 4 y + y + 3y () z = y (3) z = sin( y) (4) z = cos y (5) z = 4y (6) z = tan y (7) z = log( + y ) (8) z = tan y + + y ( ) () z = 3 8y + y z y = 4 + + 6y () z = y z y = (3) z =