Question

why is (sinωt)^3 is not Simple Harmonic Motion?

Answer 1

Because is is equal to:

\(\dfrac 14 (3 sin(\omega t)-sin(3\omega t))\), so it is a combination of two SHMs.

Answer 2

The plot looks like the attached file.
(I used WolframAlpha)

Answer 3

why does combination of 2 shms is not a shm?

Answer 4

why does combination of 2 shms is not a shm? yes my also same question

Answer 5

'SH' in SHM means Simple Harmonic, ie, only 1frequency.
In your example there are 2 different frequencies : f and 3f

Only combination of 2 (or more) SHM of SAME frequency will result in another SHM.