Two particles P and Q start from origin at the same time and execute simple harmonic motion along x-axis with same amplitude but with periods 3 sec and 6 sec respectively. The ratio of the speeds of P and Q when they meet for the first time after start is

Question

Infinity Learn · Accepted Answer

$$(2)xP=A$$  $$sin$$ $$2$$$$π$$$$3t$$  and $$xa=A$$ $$sin$$ $$2$$$$π$$$$6t$$ $$=Asin$$ π$$3t$$.$$VP=dxPdt=$$  $$2$$$$π$$$$3A$$ .  $$cos$$ $$2$$$$π$$$$3t$$  and  $$VQ=dxQdt=$$  π$$3A$$ .  $$cos$$ π$$3tWhen$$  $$xP=xQ$$,   A  $$sin$$ $$2$$$$π$$$$3t$$  $$=A$$ $$sin$$ π$$3t$$⇒     $$sin$$ π$$3t$$  $$2cos$$ π$$3$$−$$1$$ $$=0when$$    $$sin$$ π$$3t=0$$    ⇒   $$t=0when$$  $$2cos$$ π$$3$$−$$1=0$$   ⇒   $$cos$$ π$$3t=12$$  $$=$$$$cos$$ π$$3$$ ⇒  $$t=1$$  S∴  $$VPVQ=2$$$$π$$$$A3$$ .    $$cos$$ π$$3.1$$ π$$A3$$     $$cos$$ π$$3$$ $$=$$ $$2$$.  $$121/2=2$$.

Two particles P and Q start from origin at the same time and execute simple harmonic motion along x-axis with same amplitude but with periods 3 sec and 6 sec respectively. The ratio of the speeds of P and Q when they meet for the first time after start is

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