RMS values of the functions.

[ttokoro]

Electrical engneering uses RMS(Root Mean Square) values for the signal wave forms.

Using the magnitude of the waveforms to be 1, rectangilar , sine and triangle waveforms show the RMS values 1/sqrt(1), 1/sqrt(2) and s1/qrt(3), respectively.

So, find the 1/sqrt(4) and 1/sqrt(5) RMS waveforms with magnitudes = 1.

Also find the average values of each wavefrom. 

Advanced problem.
Make the f(x,n). It provides the above answers.

[Werner_E · Accepted solution]

The RMS could easily be achieved using appropriate pulse-width modulation (f1).

For the averages you demand we would have to slightly modify pulse width and magnitude (f2) 😉

[ttokoro]

Using unit step function to chop DC 1/n makes 1/sqrt(n) RMS waveform.

But we can make another waveforms such as,

If some one find new function, please share here your waveform. Any average value is ok. Only RMS of 1/sqrt(n) is need. 

Using above function we can make this waveform.