HW

Description of HW

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1

1. Solve 2nd order ODE
2. Calculate maximum value of the peak response (magnification factor) for a system with some damping ratio given (Quadrature peak picking method)
3. Solve for the forced response of a single-degree-of-freedom system to a harmonic excitation
4. Discuss the stability of 2nd order ODE
5. Find range of values for PD controller in feedback for stability
6. Compute a feedback law with full state feedback
7. Find the equilibrium points of the nonlinear pendulum equation

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2

1. Find EQM for mass-spring with dynmaic friction on incline (this is nonlinear EQM due to columb friction)
2. Modal analysis problem on 2 by 2 system
3. Find EQM using lagrangian, 2 pendulums attached by one spring between them
4. Another Modal analysis problem on 2 by 2 system
5. 2nd order system, subject to 2 impulses, find response using convolution
6. Convolution problem. Underdamped system, force is half sin

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3

1. Find EQM, one mass, 2 springs, different k, springs only attached when hit
2. Find EQM using Lagrangian, pendulum, but string is rubber band with some stiffness.
3. Find exact solution to nonlinear pendulum EQM
4. nonlinear second order ODE. Find equilibrium points and stability at these.
5. nonlinear 2nd order. Find stability around equilibrium
6. similar to above, but find stability conditions based on damping sign
7. columb damping and phase plane
8. Given phase plane equation (i.e. dy/dx), determine stability. i.e. go back from phase plane to the system matrix
9. Solve Van Der Pol using perurbation

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