IB Physics and Maths. Simple harmonic motion

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A tutorial sheet on simple harmonic motion using IB Physics and Maths skills is given below.

  1. The period of oscillation of a particle moving in simple harmonic motion is T. For what fraction of this time are the velocity and acceleration vectors in the same direction?
  2. The period of oscillation of a particle moving in simple harmonic motion is T. For what fraction of this time are the displacement from the equilibrium position and the velocity vector in the same direction?
  3. The energy of a particle moving in simple harmonic motion is E. Find the energy of the particle if its mass is doubled and the frequency of oscillation is tripled.
  4. A particle moves in simple harmonic motion of period 6.0 s and amplitude 12.0 cm. At a certain time the particle is moving away from the equilibrium position at 3.0 cm s-1. Find the time taken by the particle to come to rest.

IB Physics and Maths. Straight Line Motion

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A tutorial sheet of problems on motion in a straight line, solved using IB Physics and Mathematics skills, is given below.

  1. The acceleration of a particle is given by a = - k x2, where k is a constant. Is the motion simple harmonic motion? Explain.
  2. In question 1, k = 0.01 m-1 s-2 and the mass of the particle is 100.0 g. Using a graphical method, find the work done on the particle when it moves from x = ∛2 m to x = 0.
  3. Find the speed of the particle at the origin if it is at rest when x = ∛2 m.
  4. Show that the velocity of the particle is given by, -√( ( 2 - x3)/150 ).
  5. Using a GDC show that the time taken to reach the origin is 15.3 s.