HSC Science (Electronics) 12th Board ExamMaharashtra State Board
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Obtain the Differential Equation of Linear Simple Harmonic Motion. - HSC Science (Electronics) 12th Board Exam - Physics

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Question

Obtain the differential equation of linear simple harmonic motion.

Solution

Differential equation of linear S.H.M:
a.   Let a particle of mass ‘m’ undergo S.H.M about its mean position O. At any instant ‘t’, displacement of particle be ‘x’ as shown in the following figure.

b.   By definition, F = - kx .….................(1) 
      where, k is force constant
c.   The acceleration of the particle is given by,

     `a=(dv)/(dt)=(d(dx/dt))/dt=(d^2x)/dt^2`

d.   According to Newton’s second law of motion,
      F = ma

`therefore F=m((d^2x)/dt^2)` ...................(2)

e.   From equations (1) and (2),

 `m((d^2x)/dt^2)=-kx`

`therefore (d^2x)/dt^2=-k/mx`

`therefore (d^2x)/dt^2+k/mx=0`.....................(3)

where, `k/m=omega^2=contsant`

`therefore (d^2x)/dt^2+omega^2x=0`.....................(4)

f.   Equations (3) and (4) represent differential equation of linear S.H.M.

 

  Is there an error in this question or solution?

APPEARS IN

 2016-2017 (March) (with solutions)
Question 2.3 | 2.00 marks

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Solution Obtain the Differential Equation of Linear Simple Harmonic Motion. Concept: Differential Equation of Linear S.H.M..
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