The differential equation of all Simple Harmonic Motions of given period 2pi/n, is

1. d²x/dt² +nx=0
2. d²x/dt² + n²x=0
3. d²x/dt² -n²x=0
4. d²x/dt² + (x/n²)=0 Please answer this question someone please.

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