The differential equation of displacement of simple harmonic motions of given period 2pi/n` is

Dear pallavi

 equation of SHM is

X=Asin(wt + Φ) .............1

where w= 2*pi /T

           = 2*pi /2pi/n   =n

so X = X=Asin(nt + Φ)

differentiate

 dx/dt  =An cos(nt + Φ)

again differentiate

 d²x/dt² = -An²sin(nt + Φ)

             =n² X   (from equation 1)

d²x/dt² = -Xn²

 d²x/dt² + Xn² =0

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