Exercise

EXERCISES 2.6 [Harmonic Analysis]

1. The following values of y give the displacement in cm of a certain machine part of the rotation x of the flywheel. Expand f (x) in the form of a Fourier series.

2. The displacement f(x) of a part of a machine is tabulated with corresponding angular moment 'x' of the crank. Express f(x) as a Fourier series upto third harmonic.

3. Find the Fourier series as far as the second harmonic to represent the function given by table below :

4. Find the Fourier series upto second harmonic representing the function given by

5. Find the Fourier series upto second harmonic representing the function given by

6. Find the Fourier series upto second harmonic representing the function given by

7. Find the Fourier series upto third harmonic representing the function given by

8. Obtain the first three co-efficients in the Fourier cosine series for y, where is given in the following table.