Solve the following differential equation: y''+4y'+4y=u(t-1)-u(t-3), y(0)=0, y'(0)=0

Expert Solution

Colby Messinger answered 1 year ago

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1. The differential equation y''+4y=f(t) and y'(0)=y(0)=0 a. Find the transfer function and impulse response. b. If f(t)=u(t)-u(t-1). Find the y(t) by convolution and Laplace techniques. u(t) is unit step function. c. If f(t)= cos(t) ; find the y(t) by convolution and Laplace techniques. 2. The differential equation y''+3y'+2y=e^(-3t) and y'(0)=y(0)=0 a. Find the system transfer function and impulse response. b. Find the y(t) by convolution and Laplace techniques. 3. y''+3y'+2y=f(t) and y'(0)=y(0)=0 Plot y(t) without any calculations and write...

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