A function of time is represented as follows t+ 2 t+ 4 t . The motion represented by it is

Step-by-step solution

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, t has a period T₀= 2 2 t has a period = T₀ 2 and 4 t has a period 2 4 = T₀ 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 T₀ and thus, the sum is a periodic function with