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Mechanics, EXT2 M1 2024 HSC 5 MC

A particle is moving in simple harmonic motion with period 10 seconds and an amplitude of 8 m . The particle starts at the central point of motion and is initially moving to the left with a speed of m s, where  .

What will be the position and velocity of the particle after 7.5 seconds?

  1. At the central point of motion with a velocity of
  2. At the central point of motion with a velocity of
  3. 8 m to the left of the central point of motion with a velocity of
  4. 8 m to the right of the central point of motion with a velocity of
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Mechanics, EXT2 M1 2022 HSC 15b

The diagrams show two positions of a single piston in the cylinder chamber of a motorcycle. The piston moves vertically, in simple harmonic motion, between a maximum height of 0.17 metres and a minimum height of 0.05 metres.
 
           

The mass of the piston is 0.8 kg. The piston completes 40 cycles per second.

What is the resultant force on the piston, in newtons, that produces the maximum acceleration of the piston? Give your answer correct to the nearest newton.  (3 marks)

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♦ Mean mark 50%.

 
   

 

 
   
   
   

Mechanics, EXT2 M1 2021 HSC 13d

An object is moving in simple harmonic motion along the -axis. The acceleration of the object is given by    where is its displacement from the origin, measured in metres, after seconds.

Initially, the object is 5.5 metres to the right of the origin and moving towards the origin. The object has a speed of 8 m s as it passes through the origin.

  1. Between which two values of is the particle oscillating?  (2 marks)

  2. Find the first value of for which  ,  giving the answer correct to 2 decimal places.  (2 marks)

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i.   

♦ Mean mark 47%.

 


 

 

 

ii.   

♦♦ Mean mark 24%.


 

  

  

 

Mechanics, EXT2* M1 2007 HSC 6a

A particle moves in a straight line. Its displacement, metres, after seconds is given by

.

  1. Prove that the particle is moving in simple harmonic motion about    by showing that   .  (2 marks)

  2. What is the period of the motion?  (1 mark)

  3. Express the velocity of the particle in the form  α, where  α  is in radians.  (2 marks)

  4. Hence, or otherwise, find all times within the first    seconds when the particle is moving at metres per second in either direction.  (2 marks)

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i.   

 
 
 

 

ii. 

 

 

iii. 

α

αα
αα
α
α
 

 

α
α

 

(iv) 

 

 

Mechanics, EXT2* M1 2006 HSC 4b

A particle is undergoing simple harmonic motion on the -axis about the origin. It is initially at its extreme positive position. The amplitude of the motion is 18 and the particle returns to its initial position every 5 seconds.

  1. Write down an equation for the position of the particle at time    seconds.  (2 marks)

  2. How long does the particle take to move from a rest position to the point halfway between that rest position and the equilibrium position?  (3 marks)

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i.   

♦♦♦ “Very poorly” answered (exact data unavailable).

 

 

ii.   

 

 

Mechanics, EXT2* M1 2005 HSC 5c

A particle moves in a straight line and its position at time    is given by

  1. Express    in the form    where    is in radians.  (2 marks)

  2. The particle is undergoing simple harmonic motion. Find the amplitude and the centre of the motion.  (2 marks)

  3. When does the particle first reach its maximum speed after time  ?  (1 mark)

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i.   

 

 

 

 

ii. 
 

 

 

iii. 

 

 

Mechanics, EXT2* M1 2015 HSC 13a

A particle is moving along the -axis in simple harmonic motion. The displacement of the particle is metres and its velocity is ms. The parabola below shows as a function of .

2015 13a

  1. For what value(s) of is the particle at rest?  (1 mark)

  2. What is the maximum speed of the particle?  (1 mark)

  3. The velocity of the particle is given by the equation

           where , and are positive constants.

     

    What are the values of , and ?  (3 marks)

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i.   

 

ii.   

 

iii. 

♦ Mean mark 41%.

 
 

Mechanics, EXT2* M1 2013 HSC 12e

A particle moves along a straight line. The displacement of the particle from the origin is , and its velocity is . The particle is moving so that  , where is a constant.

Show that the particle moves in simple harmonic motion with period  .   (2 marks)

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