The condition for a function to be periodic is that it must identically repeat itself after a fixed interval of time. For a function to represent an SHM, it must have the form of cos ( or sin ( with a time period T.
(a) sin ωt – cos ωt = √2(-)..(Multiply & divide by √2 )
= √2.sin (ωt - π/4)
Hence, it is an SHM with a period 2π/ω.
(b) sin3 ωt = 1/3(3sin ωt - sin3ωt)
Each term here, sin ωt and 3ωt represent SHM. But B. is the result of superposition of two SHMs, is only periodic not SHM. Its time period is 2π/ω.
(c) It can be seen that it represents an SHM with a time period of 2π/2ω.
(d) It represents periodic motion but not SHM. Its time period is 2π/ω.
(e) An exponential function never repeats itself. Hence, it is a non periodic motion.
(f) It clearly represents a non-periodic motion.
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