Unit:12 Oscillations Syllabus ref. and Key Concepts (KC) 17.1 Simple harmonic oscillations KC1 KC3 KC4 Grade:12A2 September 2023 Week:6,7 Learning objectives Suggested teaching activities 17.1.1 Understand and use the terms displacement, amplitude, period, frequency, angular frequency and phase difference in the context of oscillations, and express the period in terms of both frequency and angular frequency. Introduce the topic by demonstrating simple harmonic oscillations with examples e.g. a pendulum, a mass on a spring, a dynamics trolley tethered by springs between two retort stands, etc. 17.1.2 Understand that simple harmonic motion occurs when acceleration is proportional to displacement from a fixed point and in the opposite direction. Ask learners to describe what they notice about these examples of motion. They may use terms from Unit 7 Waves and superposition and Unit 9 Motion in a circle to explain their observations. Define displacement, amplitude, period, frequency, angular frequency and phase difference in the context of oscillations. Relate these to learners’ understanding of terms from Unit 7 and Unit 9. Explain that simple harmonic motion occurs when acceleration is proportional to displacement from a fixed point and in the opposite direction. Ask learners to draw this relationship on an acceleration–displacement graph. Learners can demonstrate simple harmonic motion by setting up a funnel hanging from string such that it oscillates up and down. They place water or sand in the funnel and with a long piece of paper running underneath, the oscillating funnel creates a sinusoidal pattern (see spark.iop 305 link). Learners can investigate simple harmonic motion further by using the dynamics trolley tethered by springs between two retort stands and a motion sensor connected to a datalogger to track the oscillation. An oscillation circus can be set up for learners to observe more examples (see spark.iop 301 link). Introduce equations that allow description of simple harmonic motion and calculation of variables. Relate to the mathematical treatment of Unit 9 Motion in a circle. Syllabus ref. and Key Concepts (KC) Learning objectives Suggested teaching activities 17.1.3 Use a = –ω2x and recall and use, as a solution to this equation, x = x0 sin ωt. Analyse displacement–, velocity– and acceleration–time graphs and relate them to the equations. 17.1.4 Use the equations v = v0 cos ωt and v = ± ω (x02 – x2). 17.1.5 Analyse and interpret graphical representations of the variations of displacement, velocity and acceleration for simple harmonic motion. 17.2 Energy in simple harmonic motion KC3 KC4 17.2.1 Describe the interchange between kinetic and potential energy during simple harmonic motion. 17.2.2 Recall and use E = ½mω2x02 for the total energy of a system undergoing simple harmonic motion. Set learners qualitative questions on graphical representation of simple harmonic motion and quantitative questions using the equations that describe the variables of motion. (F) Learners can investigate oscillations further using the Simple Harmonic Motion simulation. (I) Teacher notes and learner worksheets from the IoP on simple harmonic motion and its mathematical treatment: https://spark.iop.org/episode-305-energy-simple-harmonic-motion https://spark.iop.org/episode-301-recognising-simple-harmonic-motion https://spark.iop.org/episode-302-getting-mathematical Simple Harmonic Motion simulation: www.physicslab.co.uk/shm.htm Ask learners to describe qualitatively what happens in terms of energy during simple harmonic motion. A simple demonstration may aid explanation as learners observe and explain what is happening e.g. a mass on a spring demonstrates the change of potential energy to kinetic energy as it bounces. Use the Energy Skate Park simulation to set up a simple harmonic oscillation of a skater on a frictionless track. The simulation can show the change in potential, kinetic and total energy as the skater moves. Learners can predict what the graph will look like before releasing the skater or you can ask them to explain the graph once it has been plotted. Introduce the equation for energy and relate to learners’ understanding of kinetic energy from Unit 5 Work, energy and power. Set learners questions for practice. (F) Teacher notes and learner worksheets from the IoP on energy in simple harmonic motion: https://spark.iop.org/episode-305-energy-simple-harmonic-motion Energy Skate Park simulation: https://phet.colorado.edu/en/simulation/legacy/energy-skate-park Syllabus ref. and Key Concepts (KC) 17.3 Damped and forced oscillations, resonance KC1 KC4 Learning objectives Suggested teaching activities 17.2.1 Understand that a resistive force acting on an oscillating system causes damping. Demonstrate examples of oscillations dying away due to friction e.g. water in a U-tube, a marble on a curved track, a skateboarder on a half pipe, etc. Introduce this loss of energy in an oscillatory system as damping. 17.2.2 Understand and use the terms light, critical and heavy damping and sketch displacement–time graphs illustrating these types of damping. Learners can investigate damped oscillations using a mass on a spring and a motion sensor connected to a datalogger (see spark.iop datalogging link). 17.2.3 Understand that resonance involves a maximum amplitude of oscillations and that this occurs when an oscillating system is forced to oscillate at its natural frequency. Explain resonance and relate to an oscillating system’s natural frequency. Ask learners to sketch the displacement–time graph for damping. Learners may identify the exponential nature of damping, but need not calculate this. Introduce light, critical and heavy damping and provide examples of each. Direct learners to sketch appropriate displacement–time graphs for each example. Learners may be interested to learn more about the uses of damping e.g. shock absorbers, dampers on fire doors, etc. They can relate these examples to the appropriate type of damping. Demonstrate Barton’s pendulums to introduce resonance. Discuss examples of forced oscillations e.g. a cyclist turning the pedal, pushing a child on a swing, etc. Show video clips of extreme cases of resonance such as a wine glass breaking, the Tacoma bridge collapse and the ‘wobbly’ Millennium Bridge in London. Set learners questions for practice. (F) Learners can investigate oscillations further using the Free and Forced Oscillations simulation. (I) Teacher notes and learner worksheets from the IoP on datalogging simple harmonic motion, damped simple harmonic motion and resonance: https://spark.iop.org/datalogging-shm-mass-spring https://spark.iop.org/episode-306-damped-simple-harmonic-motion https://spark.iop.org/episode-307-resonance Free and Forced Oscillations simulation: www.physicslab.co.uk/Pull-it.htm Past and specimen papers Past/specimen papers and mark schemes are available to download at www.cambridgeinternational.org/support (F)
