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homework1 - which the temperature of the ball is reduced to...

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EEL 3657 Homework # 1 – Assigned Tue Jan 25 - Due Mon Jan 31 Covers LDEs, modeling of simple physical systems, Laplace transforms. Assume/discover any constants, parameters, or initial conditions that you feel might help toward a good grade. Your notes and the textbook should be ample material to solve these problems. 1. A rocket is shot straight up. During initial stages of flight, it has an acceleration of 7t 2 ms . The engine cuts off at t = 10s. How high will the rocket go? 2. A copper ball is heated to 100 degrees Centigrade. Then at time t = 0, it is placed in water which is maintained at 30 degrees Centigrade. At the end of 3 minutes, the temperature of the ball is reduced to 70 degrees Centigrade. Find the time at
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Unformatted text preview: which the temperature of the ball is reduced to 31 degrees Centigrade. Hint: Newton’s law of cooling: The time rate of change of temperature T of the ball is proportional to the difference between T and the temperature of the surrounding medium. 3. Find Laplace transform of (a) t t sin (b) t 2 sin 4. Prove the final value theorem. 5. Find ) ( f and ) ( f when 2 3 5 s s F with and without using the initial value theorem. 6. Use MATLAB to find the partial-fraction expansion of the function 2 1 3 4 5 2 s s s s s F...
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