What is the frequency of #f(theta)= sin 2 t - cos 23 t #?

Question

1122 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-18T06:46:54

#1/(2pi)#.

The period of #sin 2t, P_1===(2pi)/2=pi# and

the period of #cos 23t, P_2=(2pi)/23.#

As #23P_2=2P_1=2pi#, the period P for the compounded oscillation

f(t) is the common value #2pi#, so that

#f(t+2pi).=sin(2t+4pi)- cos(23t+46pi)=sin 2t-cos 23t#

#= f(t)#. Checked that P is the least P, asf(t+P/2) is not f(t).

The frequency #= 1/P=1/(2pi)#