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Mechanics, EXT2* M1 2014 HSC 12a

 A particle is moving in simple harmonic motion about the origin, with displacement metres. The displacement is given by  , where is time in seconds. The motion starts when  .

  1. What is the total distance travelled by the particle when it first returns to the origin?   (1 mark)

  2. What is the acceleration of the particle when it is first at rest?    (2 marks)

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Mechanics, EXT2* M1 2011 HSC 3a

The equation of motion for a particle undergoing simple harmonic motion is 

 ,

where is the displacement of the particle from the origin at time , and is a positive constant.

  1. Verify that  , where and are constants, is a solution of the equation of motion.    (1 mark)

  2. The particle is initially at the origin and moving with velocity . 

     

    Find the values of and in the solution  .    (2 marks)

  3. When is the particle first at its greatest distance from the origin?   (1 mark)

  4. What is the total distance the particle travels between    and  ?   (1 mark)

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i.  
 
 
   
   

 

ii.   

  
♦♦ Mean mark part (iii) 47%
 

iii.   

 

 

iv. 

♦♦ Mean mark 22%
MARKER’S COMMENT: Many students found the displacement at rather than the distance travelled while another common error found distance as 2 x amplitude.