# HW1 - ME360 Dynamic Systems HW1 Prof Gillespie Fall 2010...

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ME360 - Dynamic Systems HW1 Prof. Gillespie - Fall 2010 ME360 - Dynamic Systems - Fall 2010 HW1 - Due Sept 9 This homework assignment is intended as a warm-up and review of physics, math (Math216), and MATLAB. For further reference, read the handout and sections 1.1, 2.1, and 3.1 of the textbook. Problem 1 Consider an electrical circuit whose behavior may be described by the 2nd order Ordinary Diﬀerential Equation (ODE): ¨ x + 9 x = 9, with x (0) = 0 and ˙ x (0) = 0. Determine which of the time functions below is the solution to this ODE. x ( t ) = 3 cos t x ( t ) = sin3 t - cos 3 t x ( t ) = 1 - cos 3 t x ( t ) = 3 - 3 sin3 t Problem 2 Consider the following ﬁrst-order diﬀerential equation ˙ x ( t ) + 1 2 x ( t ) = 5 , x (0) = 1 (1) Find the full solution x ( t ) to the diﬀerential equation. Problem 3 Use MATLAB to sketch the solution you computed above for x ( t ). Print-out and submit your m-ﬁle and the resulting ﬁgure. For a review of MATLAB, you may wish to visit the MATLAB Basics Tutorial at:

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HW1 - ME360 Dynamic Systems HW1 Prof Gillespie Fall 2010...

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