Conditions for Simple Harmonic Motion (Edexcel A Level Physics) : Revision Note

Katie M

Author

Katie M

Last updated

Conditions for Simple Harmonic Motion

  • Simple harmonic motion (SHM) is a specific type of oscillation

  • An oscillation is said to be SHM when:

    • The acceleration is proportional to the displacement

    • The acceleration is in the opposite direction to the displacement

  • Examples of oscillators that undergo SHM are:

    • The pendulum of a clock

    • A mass on a spring

    • Guitar strings

    • The electrons in alternating current flowing through a wire

13-1-examples-of-shm_edexcel-al-physics-rn
  • Time period, T:

    • The objects swings are periodic, meaning they are repeated in regular intervals according to their frequency or time period

    • If an object swings freely it always takes the same time to complete one swing

Restoring force

  • When an object is moving in SHM a force, called the restoring force, F, is always trying to return the object back to its equilibrium position. 

  • The force is proportional to the displacement, x, from that equilibrium position

F = -kx

  • Where: 

    • is the restoring force

    • x is the displacement of the object from the equilibrium position

    • k is a constant depending on the system

    • the negative sign shows that the acceleration will always be towards the centre of oscillation  

SHM pendulum, downloadable AS & A Level Physics revision notes

Force, acceleration and displacement of a pendulum in SHM

  • This is why a person jumping on a trampoline is not an example of simple harmonic motion:

    • The restoring force on the person is not proportional to their distance from the equilibrium position

    • When the person is not in contact with the trampoline, the restoring force is equal to their weight, which is constant

    • This does not change, even if they jump higher

Worked Example

A 200g toy robot is attached to a pole by a spring, with a spring constant of 90 N m-1, and made to oscillate horizontally.

(a) What force will act on the robot when it is at its amplitude position of 5 cm from equilibrium? 

(b) How fast will the robot accelerate whilst at this amplitude position? 

Answer:

Part (a) 

Step 1: Convert amplitude into m

5 cm = 0.05 m

Step 2: Substitute values into the restoring force equation

-kx = -(90) x (0.05) = - 4.5 N

Step 3: Explain the answer

A force of 4.5 newtons will act on the robot, trying to pull it back towards the equilibrium position. 

13-1-worked-example_edexcel-al-physics-rn

Part (b)

Step 1: Convert mass of robot into kg

200 g = 0.2 kg

Step 2: Substitute values into Newton's second law equation: 

F = ma

So, a space equals space F over mfraction numerator negative 4.5 over denominator 0.2 end fraction = -22.5 m s-2

Step 3: Explain the answer

The robot will decelerate at a rate of 22.5 m s-2 when at this amplitude position

Examiner Tips and Tricks

Even with this topic you must make sure you convert all quantities into standard SI units

👀 You've read 1 of your 5 free revision notes this week
An illustration of students holding their exam resultsUnlock more revision notes. It's free!

By signing up you agree to our Terms and Privacy Policy.

Already have an account? Log in

Did this page help you?

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.

Download notes on Conditions for Simple Harmonic Motion