1. Problem 1: m x(t) f(t) c k m,R c k m Figure 1 Kinetic energy: Idisc θ
SYSTEM MODELING AND ANALYSIS
Problem 1: m
x(t)
f(t) c k
In the mechanical system illustrated in Figure 1, f(t) is the input and x(t) is the generalized coordinate. Write the kinetic energy, potential energy and virtual work expressions. Obtain the governing differential equation of the system.
m,R c k m
Figure 1
Kinetic energy:
Idisc θ
Potential energy:
Virtual work: Qx

2. SYSTEM MODELING AND ANALYSIS
Lagrange’s equation for x,

3. In the mechanical system illustrated in Figure 2, moment T(t) is the input and θ(t) is the output (generalized coordinate) Assuming small angular displacements, write kinetic energy, potential energy and virtual work expressions. Obtain the equation of motion of the system.
Problem 2: m
T(t) c k 2k a
Translation
Rotation
Figure 2
Lagrange’s equation for θ,

4. Problem 3:
In the mechanical system illustrated in Figure 3, xA(t) and θ(t) are the generalized coordinates, f(t) and x1(t) are the inputs. Assume small rotations (θ <<1). Obtain the equations of motion. G
Figure 3 xB

5. x1 is not determined by the system parameters
x1 is not determined by the system parameters. It is an external input, so small variation for virtual work is taken as zero.
Lagrange’s equation for θ,

6. Lagrange’s equation for xA,