Out of the following functions representing motion of a particle which represents SHM :
(i) $y = \sin ωt - \cos ωt$
(ii) $y = \sin^{3} ωt$
(iii) $y = 5 \cos (\frac{3 π}{4} - 3 ωt)$
(iv) $y = 1 + ωt + ω^{2} t^{2}$

Question

Infinity Learn · Accepted Answer

For (i),  $$y=$$$$sin$$ ω$$t-$$$$cos$$ ω$$t=212sin$$ ω$$t-12cos$$ ωt                                 $$=2sin$$ ωt $$cos$$ π$$4-$$ $$cos$$ ωt $$sin$$ π$$4$$                                 $$=2sin$$ ω$$t-$$π$$4it$$ is SHM For (ii),  $$y=sin3$$ ωt              ∴$$sin$$ $$3$$ $$A=3$$ $$sin$$ $$A-4$$ $$sin3$$ A                $$y=143$$ $$sin$$ ω$$t-$$$$sin$$ $$3$$ωt                  $$=34sin$$ ω$$t-14sin$$ $$3$$ωtIt is superposition of two SHMs of different frequencies. So it is not SHM.For (iii),        $$y=5$$ $$cos3$$$$π$$$$4-3$$ωt

Out of the following functions representing motion of a particle which represents SHM :
(i) $y = \sin ωt - \cos ωt$
(ii) $y = \sin^{3} ωt$
(iii) $y = 5 \cos (\frac{3 π}{4} - 3 ωt)$
(iv) $y = 1 + ωt + ω^{2} t^{2}$

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Out of the following functions representing motion of a particle which represents SHM :(i) y= sin ωt-cos ωt(ii) y= sin3 ωt(iii) y= 5 cos 3π4-3ωt(iv) y=1+ωt+ω2t2

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Out of the following functions representing motion of a particle which represents SHM :
(i) $y = \sin ωt - \cos ωt$
(ii) $y = \sin^{3} ωt$
(iii) $y = 5 \cos (\frac{3 π}{4} - 3 ωt)$
(iv) $y = 1 + ωt + ω^{2} t^{2}$