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The differential equation of all Simple Harmonic Motions of given period 2pi/n, is d 2 x/dt 2 +nx=0 d 2 x/dt 2 + n 2 x=0 d 2 x/dt 2 -n 2 x=0 d 2 x/dt 2 + (x/n 2 )=0 Please answer this question someone please.

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.

Grade:12

1 Answers

Arun
25757 Points
5 years ago
Dear student
 
 

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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