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)?