Energy In Simple Harmonic Motion - Practice Questions & MCQ

A particle executing S.H.M. possesses two types of energy: Potential energy and Kinetic energy

Potential energy-

• This is an account of the displacement of the particle from its mean position.
• Formula-

 As restoring force is given as 

        So 

      using  or  

      we get     

          For   

         

• Potential energy maximum and equal to total energy at extreme positions 

      i.e 

• Potential energy is minimum at mean position

       i.e 

• The average value of potential energy with respect to t  

                  

                  

                So  

Kinetic energy-

• This is because of the velocity of the particle.
• Formula

            

       or  using   we get  

       And using   and   we get    

• Kinetic energy is maximum at the mean position and equal to total energy at the mean position.

     i.e 

• Kinetic energy is minimum at the extreme positions.

       i.e 

• The average value of kinetic energy with respect to t  

             

       

      So  

Total energy-

• Total mechanical energy = Kinetic energy + Potential energy  or E=K+U

So Total energy does not depend on position(x)  i.e. it always remains constant in SHM.

• Graph of Energy in S.H.M

At time t=0 sec, the position of the block is equal to the amplitude,