A function of time is represented as follows $\sin \omega t+\cos 2 \omega t+\sin 4 \omega t$. The motion represented by it is

This is an example of a periodic motion. It can be noted that each term represents a periodic function with different angular frequency. Since, period is the least interval of time after which a function repeats its value, $\sin \omega t$ has a period $T_0=\frac{2 \pi}{\omega}$ $\cos 2 \omega t$ has a period $\frac{\pi}{\omega}=\frac{T_0}{2}$ and $\sin 4 \omega t$ has a period $\frac{2 \pi}{4 \omega}=\frac{T_0}{4}$ The period of the first term is a multiple of the periods of the last two terms. Therefore, the smallest interval of time after which the sum of the three terms repeats is $T_0$ and thus, the sum is a periodic function with a period $\frac{2 \pi}{\omega}$.