Composition Of Two SHM - Practice Questions & MCQ

Composition of two SHM:

If a particle is acted upon by two forces such that each force can produce SHM, then the resultant motion of the particle is a combination of SHM. 

Composition of two SHM in the same direction

Let a  force  produces an SHM of amplitude  whose equation is given by 

Let another force  produce an SHM of amplitude  whose equation is given by

Now if force  is acted on the particle in the same direction then the resultant amplitude of the combination of SHM's is given by

  are the amplitude of two SHM's.  is phase difference.

Note: Here the frequency of each SHM's are the same

And the resulting phase is given by

Composition of SHM in perpendicular direction:

Let a force F₁ on a particle produces an SHM given by 

and a force F₂ alone produces an SHM given by

• Both the force F₁ and F₂ acting perpendicular on the particle will produce an SHM whose resultant is given by:

The above equation is the general equation of an ellipse. That is two forces acting perpendicular on a particle execute SHM along an elliptical path.

• When  resultant equation is given by

It is a straight line with slope

   represented by the below figure

• When  resultant equation

which is represented by below straight line with slope 

• When  resultant equation

It represents a normal ellipse

•  if  then it represents a circle