代写Engineering Math 2: Laplace Transform - Session 3 - Tutorial Questions代写C/C++语言

Engineering Math 2: Laplace Transform. - Session 3 - Tutorial Questions

Convolution Integrals

1.  Solve the following equations using the convolution theorem:

2.  For the integral equation

Using the convolution theorem/ show that:

3. Using the convolution theorem/ show that for:

Integro-Differential Equations

4. Solve the integro differential equation:

5.   Solve the integro differential equation:

Transfer Functions

6. What is the transfer function of G(s) the block diagram shown below:

Transfer function is given by:

7. A second order differential equation that defines an engineering system is given by:

If this system has a discontinuous input defined by the Dirac delta function i(t) = 4δ(t 一 2)/ find the system’s output y(t)?

8.   The transfer function of a microelectromechanical system is given as:

What is the equation of motion describing the behaviour of the system in the time domain for a sinusoidal forcing function of amplitude 3 and period = π ?

Hint: Y(s) = I(s)G(s) and we have been given the system’s input in the question. Also, so we have all the information for L一1 {I(s)}.

9.   An RC network is modelled by the equation:

where v(t) is the system response and the time varying input is e(t). Assume the initial condition V(0) = 0.

a.) Determine the transfer function G(s) for the system.

b.) What is the time response V(t) of the system for an impulse input e = δ(t)?