Question

the function y=log (wt). the displacement y increases monotonically with time t, is it periodic function or non periodic function

Answer 1

Given function,

y = log wt

Here, Displacement y increases monotonically with time t.

Let us consider it is a Periodic function y(t) = logwt

Since it's considered as a Periodic function, Let us assume it's period as some T.

So y(t + T) = y(t)

⇒ logw(t + T) = log w(t)

⇒ w(t + T) = wt

⇒ wt + wT - wt = 0

⇒wT = 0

Since w can't be zero, T = 0.

Since there is no period for this function, The function is non Periodic.