The period of a particle in SHM is $$8$$ $$sec$$. At t $$=$$ $$0$$, it is at the mean position. The ratio of the distances travelled by it in the first one second and in the $$2nd$$ one second is

Question

The period of a particle in SHM is $$8$$ $$sec$$. At t $$=$$ $$0$$, it is at the mean position. The ratio  of the distances travelled by it in the first one second and in the $$2nd$$ one second is

Infinity Learn · Accepted Answer

At t $$=$$ $$0$$, let particle move in $$+x$$ direction. So, equation of SHM is :  $$displacement=$$ $$x=Asin$$ωt given $$T=8sec$$ $$x=Asin2$$$$π$$Tt $$x=Asin2$$$$π$$$$8t---(1)$$  displacement in $$t=1$$ first second is →from equatin (1)→ $$x1=Asin2$$$$π$$$$8(1)=A12$$ displacement in $$t=2$$ two seconds is →from equatin (1)→ $$x2=Asin2$$$$π$$$$8(2)=A$$ ratio  of the distances travelled by it in the first one second and in the $$2nd$$ one second $$=$$ $$x1$$ $$x2-$$ $$x1$$ $$ratio=A2A-A2$$ $$ratio=12-1$$ rationalize ratio  of the distances travelled by it in the first one second and in the $$2nd$$ one second $$=2+1$$

The period of a particle in SHM is 8 sec. At t = 0, it is at the mean position. The ratio of the distances travelled by it in the first one second and in the 2nd one second is

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