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Obtain instantaneous velocity of a particle executing SHM.

Answer» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :Intantaneous velocity of SHM particle is the rate of change of displacement for a time interval. <br/> Suppose the displacement of SHM particle at time t with amplitude A and angular speed `omega` is <br/> `x(t)= A cos (omega t+ phi)"""……"(1)` <br/> where `phi` is the initial phase <br/> <a href="https://interviewquestions.tuteehub.com/tag/differentiating-953151" style="font-weight:bold;" target="_blank" title="Click to know more about DIFFERENTIATING">DIFFERENTIATING</a> <a href="https://interviewquestions.tuteehub.com/tag/equation-974081" style="font-weight:bold;" target="_blank" title="Click to know more about EQUATION">EQUATION</a> (1) respect to t gives the instantaneous velocity <br/> `therefore v(t)= (d[x(t)])/(dt) = (d)/(dt)[A cos (omega t+ phi)]` <br/> `therefore v(t)= -A omega sin (omega t+ phi)` <br/>but `sin(omega t +phi)= pm sqrt(1-cos^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>) (omega t+ phi))` <br/> `v(t)= (-A omega) (pm sqrt(1-cos^(2) (omega t+ phi)))` <br/> `= pm omega sqrt(A^(2)-A^(2) cos^(2)(omega t+ phi))` <br/> `= pm omega sqrt(A^(2)-x^(2)(t))` <br/> Generally `v= pm omega sqrt(A^(2) - x^(2))` <br/> Special Cases : <br/> (1) At mean position, x=0 <br/> Velocity `v= pm omega A` <br/> In +x-direction, v is positive and in -x-direction, v is negative. <br/> Hence, maximum velocity of SHM particle `v_("max")= A omega` <br/> (2) At extreme point, for velocity `x= |A|`, <br/> `v= pm omega sqrt(A^(2)-A^(2))""[therefore |A|^(2)= A^(2)]` <br/> `therefore v= 0` <br/> The velocity of SHM particle at extreme points is <a href="https://interviewquestions.tuteehub.com/tag/zero-751093" style="font-weight:bold;" target="_blank" title="Click to know more about ZERO">ZERO</a>.</body></html>


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