Jawaban nomer 2(a)

m x+c x+kx=ky+c y

Laplace dari m x+c x+kx adalah

x t( )2 sin 2 t( )

53 cos 2 t( )

10

3 e

t

4

cos31 t4

10

29 31 e

t

4

sin31 t4

310

m 2tx t( )d

d

2

ctx t( )d

d

k x t( )laplace

ts laplace x t( ) t s( ) 2 x0 0

x0x x0( )d

d

x 0( ) 2 s2 laplace x t( ) t s( ) 2 s x 0( ) 4 laplace x t( ) t s( )

k y t( ) cty t( )d

d

laplace

t2 s 1( )

s2 4

10 5 0 5 105

0

5

Grafik Respon Getaran x(t)

x t( )

t

y t( ) 0.5 cos 2t( )

0 2 4 6 8 100.6

0.4

0.2

0

0.20.4

0.6

Grafik y(t)

y t( )

t

Laplace y(t) adalah sebagai berikut : y t( )laplace

t0.5 s

s2 4

m 2 k 4 c 1

Laplace gaya eksitasi

s x s( ) 2 0 1 0 2 s2 x s( ) 2 s 0 4x s( )2 s 1( )

s2 4

solve

x s( )2 s 2

s2 4 2 s2 s 4

2 s 2

s2 4 2 s2 s 4

invlaplace

s2 sin 2 t( )

53 cos 2 t( )

10

3 e

t

4

cos31 t4

10

29 31 e

t

4

sin31 t4

310

Jawaban nomer 2(b)

m x+c x+kx=ky+c y

Laplace dari m x+c x+kx adalah

x1 0 y1 0 x2 10 y2 50

y y1y2 y1

x x1x2 x1

solve

y5 x

Y1 t( ) 5.t

x1 10 y1 50 x2 20 y2 0

y y1y2 y1

x x1x2 x1

solve

y100 5 x

Y2 t( ) 100 5t

y t( ) Y1 t( ) 0 t 10if

Y2 t( ) 10 t 20if

0 5 10 15 200

10

20

30

40

50Grafik t terhadap y(t)

y t( )

ty t( ) Y1 t( ) Y2 t( )

y t( )laplace

t100s

m 2 k 4 c 1

m 2tx t( )d

d

2

ctx t( )d

d

k x t( )laplace

ts laplace x t( ) t s( ) 2 x0 0

x0x x0( )d

d

x 0( ) 2 s2 laplace x t( ) t s( ) 2 s x 0( ) 4 laplace x t( ) t s( )

k y t( ) cty t( )d

d

laplace

t400s

Laplace gaya eksitasi

s x s( ) 2 0 1 0 2 s2 x s( ) 2 s 0 4x s( )400s

solve

x s( )400

s 2 s2 s 4

400

s 2 s2 s 4

invlaplace

s100

100 31 e

t

4

sin31 t4

31 100e

t

4

cos31 t4

x t( ) 100100 31 e

t

4

sin31 t4

31 100e

t

4

cos31 t4

0 5 10 15 200

50

100

150

200Grafik Respon Getaran x(t)

x t( )

t

Jawaban Menggunakan Mathcad

Jawaban nomer 1m 0.2 R 0.5 4000

Persamaan Getaran pada Turbin

M 2tX t( )d

d

2 c

tX t( )d

d

k X t( ) m 2 R sin t( )

Laplace ruas kiri

M 2tX t( )d

d

2 c

tX t( )d

d

k X t( )laplace

t200s laplace X t( ) t s( ) 1000 x0 0

x0X x0( )d

d

200X 0( ) 1000s2 laplace X t( ) t s( ) 1000s X 0( ) 1000laplace X t( ) t s( )

200s X s( ) 10000 2000 1000s2 X s( ) 10000 1000X s( )Laplace ruas kanan

m 2 R sin t( )laplace

t

float 5

1.9844e11

s2 1.5791e8

Laplace ruas kiri dan ruas kanan digabungkan seperti berikut200s X s( ) 10000 2000 1000s2 X s( ) 10000 1000X s( )

1.9844e11

s2 1.5791e8

solve

X s( )1.9844e11

s2 1.5791e8 1000.0s2 200.0s 1000.0 X s( )

1.9844e11

s2 1.5791e8 1000.0s2 200.0s 1000.0 X s( )

invlaplace

s

float 5

1.5916e-9 cos 12566.0t( ) 0.0001 sin 12566.0t( ) 1.5916e-9cos 0.99499t( ) e 0.1 t 1.263sin 0.99499t( ) e 0.1 t

X t( ) 1.5916e-9 cos 12566.0t( ) 0.0001 sin 12566.0t( ) 1.5916e-9cos 0.99499t( ) e 0.1 t 1.263sin 0.99499t( ) e 0.1 t

0 10 20 30 40 501

0.5

0

0.5

1

1.5Grafik Respon Getaran Turbin X(t)

X t( )

t