1. The differential equation y''+4y=f(t) and y'(0)=y(0)=0 a. Find the transfer function and impulse response. b....

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 down your reasons!

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

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

Define:

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

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

Expert Solution

Since you have given many parts so I have answered the first 4 parts

Colby Messinger answered 2 years ago

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