When a body is in S H M , then match the following. List   -   I List   -   II A…

When a body is in SHM, then match the following.

List - I List - II
A Velocity is maximum I Acceleration is maximum
B KE is 34th  of total energy II At mean position
C PE is 34th of total energy III At half of the amplitude
D Acceleration is maximum IV At 32 times the amplitude

 

  1. A B C D
    III I IV II

     

  2. A B C D
    I III IV II

     

  3. A B C D
    II III IV I

     

  4. A B C D
    II I IV III

     

Solution

In S.H.M.
If equation of S.H.M. is given byy=Asinωt
Velocity v=ωA2-x2
And Acceleration a=-ω2x
Here ω is angular frequency and x is displacement from mean position.

From velocity equation we can see that velocity will be max when x=0 i.e. particle is at mean position.

From acceleration equation we can see that acceleration is maximum at when particle is at extreme position i.e. x=A.
Kinetic energy is 12mv2=mω22A2-x2
Hence, Kinetic energy will be 34th of maximum kinetic energy12mω2A2 when displacement is equal to half of amplitudeA.

Potential energy is given by12mω2x2
Hence potential energy will be 34th of the maximum potential energy12mω2A2 , when displacement from mean position is equal to 32A.

Asked in: AP EAMCET 2019 (21 Apr Shift 2)

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