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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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