am trying to compute the period of the following:
$$\cos(\pi t) + 2\cos(3\pi t) + 3\cos(5\pi t)$$
I know that given two sinusoids, the period is found from the ratio of the two sinusoids. but here:
$$\text{(period of the first term) }T_1 = 2$$
$$\text{(period of the second term) }T_2= 2/3$$
$$\text{(period of the third term) }T_3= 2/5$$
but where should I go from here. Can somebody please show me a general formula
whenever I encounter a question that asks for the period of the product or sum of multiple sinusoids. Thanks in advance.
Best Answer
$$2,\frac{2}{3},\frac{2}{5}\to\\\dfrac{30}{15},\dfrac{10}{15},\dfrac{6}{15}\\$$now factor $\dfrac{2}{15}$so $$T_{total}=\dfrac{2}{15}\underbrace{[15,5,3]}_{lcm}=\\\dfrac{2}{15}\times3\times5=2$$