text: # Basics of Simple Harmonic Motion
  
  It's only fair to share...
  
  Simple harmonic motion occurs when motion in a circle with uniform acceleration is projected on a line through the centre of the circle. The motion is most naturally projected onto the x and y axes.
  
  Suppose the motion is projected onto the– axis. Then (1)
  
  We can differentiate to obtain the velocity: (2)
  
  and again to get the acceleration: (3)
  
  We can write (3) asso
  
  This is often taken as the basic equation of simple harmonic motion, and means that the the acceleration is proportional to the acceleration, but directed towards the zero point on the– axis.
  
  We can use the identityto obtain further equations.
  
  From (1)and from (2)
  
  Substituting these into the identity gives
  
  Similarly for projection onto the– axis: (4)
  
  We can differentiate to obtain the velocity: (5)
  
  and again to get the acceleration: (5)
  
  We can write (5) asso
  
  We can use the identityto obtain a further equation.
  
  From (4)and from (5)
  
  Substituting these into the identity gives
  
  If the frequency isthenso we can also write
  
  andwith corresponding equations for
explanation: The document provides a detailed explanation of simple harmonic motion, including the mathematical derivation of the equations for displacement, velocity, and acceleration. It does not contain a specific question or a question-and-answer pair.
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distilabel_metadata.content: # Basics of Simple Harmonic Motion
  
  It's only fair to share...
  
  Simple harmonic motion occurs when motion in a circle with uniform acceleration is projected on a line through the centre of the circle. The motion is most naturally projected onto the x and y axes.
  
  Suppose the motion is projected onto the– axis. Then (1)
  
  We can differentiate to obtain the velocity: (2)
  
  and again to get the acceleration: (3)
  
  We can write (3) asso
  
  This is often taken as the basic equation of simple harmonic motion, and means that the the acceleration is proportional to the acceleration, but directed towards the zero point on the– axis.
  
  We can use the identityto obtain further equations.
  
  From (1)and from (2)
  
  Substituting these into the identity gives
  
  Similarly for projection onto the– axis: (4)
  
  We can differentiate to obtain the velocity: (5)
  
  and again to get the acceleration: (5)
  
  We can write (5) asso
  
  We can use the identityto obtain a further equation.
  
  From (4)and from (5)
  
  Substituting these into the identity gives
  
  If the frequency isthenso we can also write
  
  andwith corresponding equations for
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides a detailed explanation of simple harmonic motion, including the mathematical derivation of the equations for displacement, velocity, and acceleration. It does not contain a specific question or a question-and-answer pair.
  
  Label: no-question