The displacement of a particle is represented by the equation y $$=$$ $$sin3$$ ωt. The motion is

Question

The displacement of a particle is represented by the equation y $$=$$ $$sin3$$ ωt. The motion is

Infinity Learn · Accepted Answer

Given equation of motion isy $$=$$ $$sin3$$ ωt     $$=$$ (3$$ $$sin$$ ωt $$-$$ $$4$$ $$sin$$ ω$$t)4$$                                                 [∵ $$sin$$ $$3$$ θ $$=$$ $$3$$ $$sin$$ θ $$-4$$ $$sin3$$ θ]⇒dydt $$=$$ [$$ddt(3$$ $$sin$$ ω$$t)-ddt(4$$ $$sin$$ $$3$$ω$$t)]$$4$$⇒$$4dydt$$ $$=$$ $$3$$ω $$cos$$ ωt $$-$$ $$4$$ ×[$$3$$ω $$cos$$ $$3$$ωt]⇒$$4$$ ×$$d2ydt2$$ $$=$$ $$-3$$ ω$$2$$ $$sin$$ ωt $$+$$ $$12$$ω $$sin$$ $$3$$ωt⇒$$d2ydt2$$ $$=$$ $$-3$$ω$$2$$ $$sin$$ ωt $$+12$$ω $$sin$$ $$3$$ω$$t4$$⇒  $$d2ydt2$$ is not proportional to y.

The displacement of a particle is represented by the equation $y = \sin^{3} ωt$ . The motion is

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The displacement of a particle is represented by the equation y = sin3 ωt. The motion is

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The displacement of a particle is represented by the equation $y = \sin^{3} ωt$ . The motion is