# Calculating the period of a harmonic function

1. Aug 20, 2011

### No0bzDown

For a example, x=16cos(10t+5π/3) ,S.I.

How am i supposed to calculate the period?(in order to do the graph)

2. Aug 20, 2011

### uart

You cos function repeats when 10t increased by $2 \pi$. See if you can work it out based on that.

3. Aug 20, 2011

### No0bzDown

If we have something like this: f(x) = cos(at)

then T= 2π/a

But i really want to know if on my first example 5π/3 is playing any role on this formula.

I mean if x=16cos(10t + 5π/3)

Is period still T = 2π/a = 2π/10 ?

4. Aug 20, 2011

### uart

Yes it is. The phase constant (5 Pi /3) does not change the frequency or period.

5. Aug 20, 2011

### No0bzDown

Nice. Thanks very much.

6. Sep 3, 2011

### gongo88

What if you have a harmonic function with both cos and sin?

such as: x(t)=4sin(15t)-3cos(9t+1.1)

can you find the period of this analytically? I have found this has a period of 2.1 by plotting it in MATLAB, but can't figure out how to calculate this analytically...

Last edited: Sep 3, 2011