Question

A body executes SHM with an amplitude 10 cm and period 2 s.Calculate the velocity and acceleration of the body when the displacement isi) zeroii) 6 cm.

Answer 1

displacement x =  A sin (ω t + Ф)  of the particle in SHM with angular frequency ω and initial phase Ф and the amplitude of oscillation  A.
     ω = 2π / T = π rad/sec

  x  = 10  Sin (π t + Ф)

if displacement is 0,  then  Sin (π t + Ф) = 0  and  Cos (ω t + Ф) = 1
So  v = dx / dt =  10 * π Cos (π t + Ф)  cm/sec
         = 10 π cm /sec
     a = d v / dt  =  - 10 π²  Sin (10 π t + Ф)
             = 0

if the displacement is 6 cm :  Sin (ωt + Ф) =  6/10 = 3/5 
     so    cos (ω t + Ф) =  4/5
  so  v =  10 π * 4/5  = 8 π cm /sec
     a =  10 π²  * Sin (π t + Ф) =  10 π² * 3/5  = 6 π²  cm/sec²