Physics-
General
Easy

Question

Consider the following statements:
The total energy of a particle executing simple harmonic motion depends on its
i) Amplitude
ii) Period
iii) Displacement
Of these statements

  1. I and II are correct    
  2. II and III are correct    
  3. I and III are correct    
  4. I , II and III are correct    

The correct answer is: I and II are correct


    Potential energy of particle in SHM
    U equals fraction numerator 1 over denominator 2 end fraction m omega to the power of 2 end exponent x to the power of 2 end exponent
    or U equals fraction numerator 1 over denominator 2 end fraction m open parentheses 2 pi f close parentheses to the power of 2 end exponent x to the power of 2 end exponent
    or U equals 2 pi to the power of 2 end exponent m f to the power of 2 end exponent x to the power of 2 end exponent…(i)
    Kinetic energy of particle in SHM
    K equals fraction numerator 1 over denominator 2 end fraction m omega to the power of 2 end exponent left parenthesis A to the power of 2 end exponent minus x to the power of 2 end exponent right parenthesis
    or K equals 2 pi to the power of 2 end exponent m f to the power of 2 end exponent left parenthesis A to the power of 2 end exponent minus x to the power of 2 end exponent right parenthesis…(ii)
    Hence, total energy
    E equals K plus U equals 2 pi to the power of 2 end exponent m f to the power of 2 end exponent x to the power of 2 end exponent plus 2 pi to the power of 2 end exponent m f to the power of 2 end exponent left parenthesis A to the power of 2 end exponent minus x to the power of 2 end exponent right parenthesis
    equals blank 2 pi to the power of 2 end exponent m f to the power of 2 end exponent A to the power of 2 end exponent equals fraction numerator 2 pi to the power of 2 end exponent m A to the power of 2 end exponent over denominator T to the power of 2 end exponent end fraction open parentheses because blank T equals fraction numerator 1 over denominator f end fraction close parentheses
    Thus, it is obvious that total energy of particle executing simple harmonic motion depends on amplitude (A) and period (T).

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