Time period (T) and amplitude (A) are same for two particles which undergo SHM along the same line. At one particular instant, one particle is at phase $$3$$$$π$$$$2$$ and other is at phase zero. While moving in the same direction. Find the time at which they will cross each other:

Question

Time period (T) and amplitude (A) are same for two particles which undergo SHM along the same line. At one particular instant, one particle is at phase $$3$$$$π$$$$2$$ and other is at phase zero. While moving in the same direction. Find the time at which they will cross each other:

Infinity Learn · Accepted Answer

At phase $$3$$π$$/2$$,$$($$ω$$t+$$ϕ$$)=3$$π$$/2$$                  $$x1=Asin$$⁡$$3$$$$π$$$$2=$$−$$Ax2=0$$ So, at $$t=0$$,$$x1=$$−Acos⁡ωt and $$x2=Asin$$⁡ω$$tx1=x2$$−$$cos$$⁡ω$$t=$$$$sin$$⁡ωt⇒$$tan$$⁡ω$$t=$$−$$1$$ω$$t=3$$$$π$$$$4$$⇒$$2$$$$π$$$$Tt=3$$$$π$$$$4$$  or  $$t=3T/8$$

Time period (T) and amplitude (A) are same for two particles which undergo SHM along the same line. At one particular instant, one particle is at phase $\frac{3 π}{2}$ and other is at phase zero. While moving in the same direction. Find the time at which they will cross each other:

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Time period (T) and amplitude (A) are same for two particles which undergo SHM along the same line. At one particular instant, one particle is at phase 3π2 and other is at phase zero. While moving in the same direction. Find the time at which they will cross each other:

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Time period (T) and amplitude (A) are same for two particles which undergo SHM along the same line. At one particular instant, one particle is at phase $\frac{3 π}{2}$ and other is at phase zero. While moving in the same direction. Find the time at which they will cross each other: