# Math Help - Period of signal

1. ## Period of signal

Stuck on the following problem, aint sure how to work out the signal of a composed sinusoid

given that $x(t) = cos(600\pi t)$ and $m(t) = 4 + 3cos(20\pi t)$ what is the period (if any) of the resulting signal

Also the signal $x(t) = 10cos(600\pi t + \frac{\pi}{3}) + 6cos(900\pi t - \frac{\pi}{4}) - 4cos(1500\pi t)$ whats the period of the signal

Im not sure how to calculate the period when theres more than one sinusoid wave

Any help most appreciated

2. Originally Posted by jordanrs
Stuck on the following problem, aint sure how to work out the signal of a composed sinusoid

Also the signal $x(t) = 10cos(600\pi t + \frac{\pi}{3}) 6cos(900\pi t - \frac{\pi}{4}) - 4cos(1500\pi t)$ whats the period of the signal

Im not sure how to calculate the period when theres more than one sinusoid wave

Any help most appreciated
First question snipped as it not complete.

The product of two sinusoids has sinusoidal components at the sum and diffrence frequencies. This for some amplitudes (non-zero) and phases is:

$x(t)=A\sin(300\pi t+\phi_1)+B\sin(1500\pi t+\phi_2)$

and since the larger period is an integer multiple of the smaller the final period is $1/150$ s

CB

3. Originally Posted by jordanrs
Stuck on the following problem, aint sure how to work out the signal of a composed sinusoid

given that $x(t) = cos(600\pi t)$ and $m(t) = 4 + 3cos(20\pi t)$ what is the period (if any) of the resulting signal

Also the signal $x(t) = 10cos(600\pi t + \frac{\pi}{3}) 6cos(900\pi t - \frac{\pi}{4}) - 4cos(1500\pi t)$ whats the period of the signal

Im not sure how to calculate the period when theres more than one sinusoid wave

Any help most appreciated

when $y(t) = x(t)m(t)$ and $x(t) = cos(600\pi t)$ and $m(t) = 4 + 3cos(20\pi t)$ what is the resulting period of $(y(t))$

also i still dont get how to calculate the periodm i dont see where you got 1/150 s from

4. Originally Posted by jordanrs
when $y(t) = x(t)m(t)$ and $x(t) = cos(600\pi t)$ and $m(t) = 4 + 3cos(20\pi t)$ what is the resulting period of $(y(t))$