# 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.

1
by TaptiSood141

2015-09-21T23:21:30+05:30

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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

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