Period of Simple Harmonic Oscillators (Edexcel International A Level (IAL) Physics): Revision Note

Exam code: YPH11

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Katie M

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Period of a simple pendulum

  • A simple pendulum is: 

    • an object moving from side to side

    • attached to a string which is fixed to a point above 

  • The period of a simple pendulum can be calculated using the equation:

T space equals space 2 straight pi square root of l over g end root

  • Where: 

    • l = the length of the pendulum

    • g = the gravitational field strength on the planet on which the pendulum is set up

Worked Example

A child is sitting on a swing that is 200 cm long. What is the period of oscillation?

Answer:

Step 1: Convert length to meters

200 cm = 2 m

Step 2: Substitute the correct values

= 2πsquare root of l over g end root= 2πsquare root of fraction numerator 2 over denominator 9.81 end fraction end root=2.84 s 

Step 3: Confirm the answer

The time period of 1 oscillation of the swing is 2.84 s

Period of a Mass-Spring System

  • A mass-spring system is:

    • an object moving up and down, or side to side 

    • attached to the end of a spring

13-3-mass-spring-example_edexcel-al-physics-rn
  • The equation for the restoring force in SHM is the same as the equation for Hooke's law

F space equals space minus k x

  • The time period T can be calculated using the equation:

T space equals space 2 straight pi square root of m over k end root

  • Where: 

    • m = the mass of the object on the end of the spring

    • k = the spring constant of the spring

Observing the Motion of a Mass-Spring System

  • An experimental and graphical method can be used to observe the motion of a simple mass-spring system

    • Tie a pencil together with the mass and set the mass in free oscillations by displacing it downwards slightly

  • The oscillations will move the pencil up and down

    • On a piece of graph paper, allow the pencil to trace the path of the oscillations by pulling the paper sideways as the mass-spring system oscillates up and down

  • The oscillations will produce a curved, periodic graph

    • This will decrease in amplitude as the mass-spring system slows down

Mass and spring experiment, downloadable AS & A Level Physics revision notes

The motion of an oscillator can be observed through a simple mass-spring system

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Katie M

Author: Katie M

Expertise: Physics Content Creator

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.