3. Consider the ODE of a pendulum i + by + a sin y = = 0. (a) Using appropriate state variables, write this pendulum equ

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3. Consider the ODE of a pendulum i + by + a sin y = = 0. (a) Using appropriate state variables, write this pendulum equ

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3 Consider The Ode Of A Pendulum I By A Sin Y 0 A Using Appropriate State Variables Write This Pendulum Equ 1
3 Consider The Ode Of A Pendulum I By A Sin Y 0 A Using Appropriate State Variables Write This Pendulum Equ 1 (112.89 KiB) Viewed 26 times
3. Consider the ODE of a pendulum i + by + a sin y = = 0. (a) Using appropriate state variables, write this pendulum equation as a sys- tem of two first order differential equations. (4 marks) (b) Find all fixed points of the two dimensional system where x1 € [0, 21 [. (2 marks) (c) Calculate the Jacobian matrix. (4 marks) (d) Calculate the eigenvalues for the fixed points as a function of a and b. (4 marks) (e) For a = 1, describe what happens for the fixed points at different values of b. (6 marks) (Total: 20 marks)
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