A Particle Executes SHM Of Amplitude 25 Cm And Time Periods 3 S. What Is The Minimum Time Required For The Particle To Move Between Two Points Located At 12.5 Cm On Either Side Of The Mean Position?

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Question

A particle executes SHM of amplitude 25 cm and time periods 3 s. what is the minimum time required for the particle to move between two points located at 12.5 cm on either side of the mean position?

Solution

Correct option is

0.5 s

Let A and B be the two extreme positions of the particle with O as the mean position. Displacements to the right of O are taken as positive while those to the left of O are taken as negative

                                                    

Let the displacement of the particle is SHM be given by 

                                             ..(i)

let us suppose that at time t = 0, the particle is at extreme position B. Setting x = A and t = 0 in Eq. (i) we have

                    A = A sin Ï•  

Giving          

  

                  

Where        A = 25 cm. 

Now let us say that the particle reaches point C at t = t1 and point D at t =t2. At C, the displacement x(t1) = + 12.5 cm and at D, it is x(t2) = –12.5 cm (see fig.) so from (ii) we have

                          

                

  

  

Notice that cos ωt2 = –0.5 even for  This value of t2 does not correspond to the minimum time because this is the time at which the particle, moving to left, reaches A and then returns to D.

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