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Unformatted text preview: the rate of change of this angle. Finally, u is the torque applied to the lower end of the beam. Suppose that the mass of the ball m = 1 kg , g = 10 m/s 2 , J = 1 kg m 2 . Check the controllability properties of this system and explain what it means in your own words. Figure 1: By rotating the beam, we can change the position of the ball on it. 3. The impulse response of an LTI system is measured to be h ( t ) = e 2 t u ( t ), where u ( t ) is the unit step signal. What is the response of the system to x ( t ) = ramp( t )? (Zero initial conditions are assumed.) 4. Suppose that the impulse response of an LTI physical system is approximately measured to be h ( t ) = e-7 t cos(2 t ) u ( t ), where u ( t ) is the unit step signal. What is the response of the system to the signal x ( t ) = 7 u ( t )? (Zero initial conditions are assumed.) 1...
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- Summer '08