When the displacement of a mass on a spring in simple harmonic motion is A/2 from the equilibrium position, what fraction of the total mechanical energy is kinetic energy?

The ratio is  KE : TM  =  0.75

Explanation:

from the question we are told that

  The displacement of a mass on a spring in simple harmonic motion is A/2 from the equilibrium position

Generally the total mechanical  energy of the mass is mathematically represented as

Here  k is the spring constant  ,  A is the total displacement of the  the mass  from maximum  compression to maximum extension of the spring

Generally this total mechanical energy is mathematically represented as

=>    

Here the potential  energy of the mass is mathematically represented as

Here x is the displacement of the mass from maximum compression or extension of the spring to equilibrium position and the value is  

So

So

=>    

=>    

So the ratio of   is  mathematically represented as

=>    

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