1.To introduce some common examples of simple harmonic motion 2.To define some common terms such as period and frequency 3.To think about the phase relationship.

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Presentation transcript:

1.To introduce some common examples of simple harmonic motion 2.To define some common terms such as period and frequency 3.To think about the phase relationship between displacement, velocity, force & acceleration Book Reference : Pages 34-35

There are many examples of simple harmonic motion, (SHM) in every day life & this topic connects well with earlier work on waves & circular motion. Examples : Child on a swing Child on a swing A mass on a spring A mass on a spring A simple pendulum A simple pendulum A boat rocking side to side on water A boat rocking side to side on water A ball rolling from side to side in a dish A ball rolling from side to side in a dish

Consider the example of a child on a swing : Equilibrium Position Maximum Displacement One complete swing is from maximum height on one side, through the lowest point to the highest point on the other side

The child on the swing is said to oscillate about the equilibrium point. The child moves repeatedly through the equilibrium point first one way and then the other Definitions : Amplitude : Is the maximum displacement from the equilibrium position Period (T) : Time for one complete oscillation Frequency (f) : Number of oscillations per second [VPL : SHM]

Imagine two identical twins swinging on adjacent identical swings... Since the swings are identical their oscillation motion will also be the same However, they oscillate out of phase, one twin reaches the maximum displacement point  t seconds behind the other The phase difference remains the same & can be described as a fraction of the whole cycle  t/T Phase difference in radians = 2  t/T

Think of two further everyday examples of SHM Describe the motion of a bungee jumper after he leaves the platform: a.Initially describe it for an ideal world, (in a vacuum with a perfectly elastic rope) b.Secondly describe what is observed in the real world and account for the differences between ideal and real world scenarios

A mass on a spring is displaced and takes 9.6s to complete 20 complete oscillations. Calculate: The time period & frequency of oscillation Consider two identical pendulums, (X & Y) which complete 20 complete cycles in 16s. What is the phase difference if: a.X passes through equilibrium 0.2s later than Y in the same direction b.X & Y both reach maximum displacement at the same time but in opposite directions

What causes a displaced object to return towards the equilibrium position? When is the velocity of the object at a maximum? When is the velocity of the object at a minimum? Is the velocity constant or does it change based upon some other factor?

For a swing complete the following table with relative size and direction Swing Position DisplacementVelocityForceAcceleration Maximum (left) Centre Maximum (Right)