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  3. 1. the differential equation y''+4y=f(t) and y'(0)

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)....

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Advance Math

1. The differential equation y''+4y=f(t) andy'(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 Laplacetechniques. u(t) is unit step function.

c. If f(t)= cos(t) ; find the y(t) by convolution and Laplacetechniques.

2. The differential equation y''+3y'+2y=e^(-3t) andy'(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) andy'(0)=y(0)=0

Plot y(t) without any calculations and write down yourreasons!

4. y''-4y'+3y=f(t) andy'(0)=y(0)=0

If f(t)=u(t)-u(t-1). Find the y(t) by convolution and Laplacetechniques. u(t) is unit step function.

Define:

a. f(t)'s system input, and y(t)'s system output. How to defineTransfer function? Find the transfer function.

b. Find y(t) by Laplace Transformation Technique.

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