A particle starts its SHM on a line at initial phase of π$$/6$$.It reaches again the point of start after time t. lt crosses yet another point P on the same line at successive intervals $$2t$$ and $$3t$$ respectively. Find the amplitude of the motion, if the particle crosses the point of start at speed $$2$$ $$m/s$$:

Question

A particle starts its SHM on a line at initial phase of π$$/6$$.It reaches again the point of start after time t. lt crosses yet another point P on the same line at successive intervals $$2t$$ and $$3t$$ respectively. Find the amplitude of the motion, if the particle crosses the point of start at speed $$2$$ $$m/s$$:

Infinity Learn · Accepted Answer

$$x=Asin$$⁡ω×$$0+$$π$$6=Asin$$⁡π$$6=A2$$ (t=0$$ at initial phase $$)Let$$ time $$t=0$$ is considered from point Q where displacement $$=A/2$$ Time period $$T=tQA+tAQ+tQP+tPQ+tPB+tBP=t+$$[$$(2t$$−$$t)+(2t$$−$$t)]$$+t=4t=2$$π$$/$$ωω$$=$$π$$/2t$$;$$x=Asin$$⁡ω$$t+$$π$$6dxdt=A$$ω$$cos$$⁡ω$$t+$$π$$6=A$$ω$$cos$$⁡π$$2+$$π$$62=A$$×π$$2t$$×$$12$$ $$($$ sign not considered $$)$$;$$A=8t$$π

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A particle starts its SHM on a line at initial phase of π/6.It reaches again the point of start after time t. lt crosses yet another point P on the same line at successive intervals 2t and 3t respectively. Find the amplitude of the motion, if the particle crosses the point of start at speed 2 m/s:

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