In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position. A. 1 4 B. 1 3 C. 1 2 D. 3 4

Question

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position. A.       1    4   B.       1    3   C.       1    2   D.       3    4

Emilee Randall · Accepted Answer

The formula for the total mechanical energy of a simple harmonic oscillation is  T  .  E  =      1    2    m            ω        2        A    2  The kinetic energy of simple harmonic oscillation at agiven position is given by,  K  .  E  =      1    2    m            ω        2    (      A    2    −      x    2    )Here,   x  =      A    2    ⇒  K  .  E  =      1    2    m            ω        2    (      A    2    −            A      2        4    )  ⇒  K  .  E  =      1    2    m            ω        2    (            3              A        2              4    )  ⇒  K  .  E  =      3    4    (      1    2    m            ω        2        A    2    )  ⇒            K      .      E              T      .      E        =      3    4  Hence, option (B) is correct.

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position. A. 1/4 B. 1/3 C. 1/2 D. 3/4

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