A body of mass 10 g vibrating with SHM of amplitude 24cm and period 4s .the coor

Question

A body of mass 10 g vibrating with SHM of amplitude 24cm and period 4s .the coordiante is +24cm when t=0 compute
a)the position of the body when t=0.5 sec b)the magnitude and the direction of the force action on thebody whne t=0.5 s c)the minimium time required for the bidy to move frominitial position to to the point where x=-12cm d)the velocity of the body when x=-12cm A body of mass 10 g vibrating with SHM of amplitude 24cm and period 4s .the coordiante is +24cm when t=0 compute
a)the position of the body when t=0.5 sec b)the magnitude and the direction of the force action on thebody whne t=0.5 s c)the minimium time required for the bidy to move frominitial position to to the point where x=-12cm d)the velocity of the body when x=-12cm

Explanation / Answer

So it is vibrating between 12 to 36 frequency=1/T =0.25 so =/2 so the motion can be written as 24cos(t/2) so when t=0.5 it is at 24/2 =16.97cm andwe know that in SHM      F=-kx so it's direction is along -ve x-axis and it's magnitude is = mw2x=0.01*(2/4)*0.1697 =4.18 *10-3 N and so x =-12 =24cos(t/2) cost/2 =-1/2 so t/2 = /2+/6   so t =1+1/3 =1.33sec for velocity v=-24(/2)sin(/2)t =-63

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