HOMEWORK 01B

Lagrange Equation

Problem 1:

Problem 2:

Problem 3:

Homework 01A, The solution of Problem 1 gives the expressions of kinetic energy, potential energy and virtual work as follows;

Problem 1:

Click for answer.

2222

1 RxmR

2121xm

21xm

21E

22

2 kx21kx

21E x)xc2f(W

Here, f(t) is the input, x(t) is the generalized coordinate. Find the equation of motion of the system by applying Lagrange equation.

fkx2xc2x2m5

222

1 mL121

21

6Lm

21E

22

2 3L2k2

21

3Lk

21E

9cLTW

2

Click for answer.

TkL9cL

9mL 2

22

Homework 01A, The solution of Problem 2 gives the expressions of kinetic energy, potential energy and virtual work as follows;

Problem 2:

Here, T(t) is the input, θ(t) is the generalized coordinate. Find the equation of motion of the system by applying Lagrange equation.

A2

A2

A2

x9/kL113/kL3/kLk5.0x

9/cL113/cL3/cLc5.0x

3/mL400m

111

11

xmL2x)3/cL4(x)3/kL4(Lfxc5.0kx5.0

Homework 01A, The solution of Problem 3 gives the expressions of kinetic energy, potential energy and virtual work as follows;

Problem 3:

Here, f(t) and x1(t) are the inputs, xA(t) and θ(t) are the generalized coordinates. Find the equation of motion of the system by applying Lagrange equation.

Click for answer.

2A

222

11 xm21mL4

121

21

2Lxm4

21E

2

1A2

1212 3

L2xx)k5.0(21)Lx(k

21kx

21E

3L2xx

3cL)Lx(cLfLx

3L2xxc5.0W 1A1A1A