# Finding the period of trig series analytically?

1. Sep 3, 2011

### gongo88

Is there a way to calculate the period of a trigonometric series (like the one below) analytically?

x(t)=5sin(16t)-4cos(8t+3.1)

2. Sep 3, 2011

### mathman

The period in this case can be gotten from: 8t = 2π or t = π/4. This works since the other term has a period 16t = 2π or t = π/8 which is a harmonic.

3. Sep 3, 2011

### gongo88

Sorry, I'm still confused. For this example...

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

...I have graphed this in MATLAB, and graphically found a period of about 2.1. I am trying to apply what you suggested, but can't figure out how to calculate the period of 2.1...

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4. Sep 3, 2011

### LCKurtz

The sum of two periodic functions will be periodic it the two periods are commensurable. That means the ratio of their periods is a rational number. And in that case, the period is the least common multiple of the individual periods. For non-integers p and q, the LCM is the least number z such that ap = z and bq = z for a and b integers.

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