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### A6     Recognise the properties of complex waves in terms of odd & even symmetry and cycle repetition.   Question 1 Statewhich symmetry and harmonics are likely to be present (odd, even or both)in Fi

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A6     Recognise the properties of complex waves in terms of odd & even symmetry and cycle repetition.

Question 1
Statewhich symmetry and harmonics are likely to be present (odd, even or both)in Figures 1 to 5 below. State also whether there are any phase shifts (+/- /2 or +/- ) and their approximate periodicity.                       `[1 mark each]
Figure 1           &nbs...

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Question Preview:

A6     Recognise the properties of complex waves in terms of odd & even symmetry and cycle repetition.

Question 1
Statewhich symmetry and harmonics are likely to be present (odd, even or both)in Figures 1 to 5 below. State also whether there are any phase shifts (+/- /2 or +/- ) and their approximate periodicity.                       `[1 mark each]
Figure 1                        Figure 2

Figure 3                         Figure 4

Figure 5

B4       Analyse complex waves using Fourier series.
C2       Synthesise a complex wave from its Fourier equation.

Question 2

a)  Obtain the Fourier series up to the 11th harmonic for the function defined by:

Assume periodicity of the function outside of the given range.        [3]
b) Comment on the characteristics of the Fourier series coefficients     [1]
Question 3

a)Obtain the Fourier series up to the9th harmonic for the following function of period 2π.                                               [3]

b)Using the series obtained in a) plot the function up to the 9th harmonic over a period of 2π (using the tabular method).                              [10]

A7       Use Laplace transforms to represent transient circuits in the s-plane.
B5       Apply transient analysis to first and second order series and parallel circuits.
C3       Evaluate the circuit response to given inputs for first and second order systems.

Question 4
A coil of 4Ω and inductance 100mH is connected in parallel with a 10Ω resistor. The whole combination is then connected in series with a 15Ω resistance and a 10V step input source. Assuming zero initial conditions, provide:
a)An s-plane representation of the circuit diagram                [1]
b)A Laplace representation of the circuit current                    [2]
c)A time-domain equation of the circuit current                    [3]
d)A time-domain expression for the inductor voltage                [3]
e)An evaluation of main current behaviour                        [2]

Question 5
A series circuit consists of a 10Ω resistance, 500mH inductance and a 10µF capacitor that are connected via single pole switch to a 1V step input. Assuming zero initial conditions when the switch is closed, provide:
a)ans-plane representation of the circuit diagram                 [1]
b)a Laplace representation of the circuit impedance                [2]
c)a time-domain equation of the current flowing in the circuit            [3]
d)a time-domain expression for the capacitor voltage                [3]
e)an evaluation of the damping state of the circuit. Suggest modifications that could change the damping behaviour.                        [2]

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