## Overview This topic covers the physical and mathematical treatment of undamped simple harmonic motion. It investigates the energy interchanges which occur during simple harmonic motion. ## Working Scientifically The specified practical work in this unit contains opportunities for learners to safely and correctly use a range of practical equipment and materials; to follow written instructions; to make and record observations; to present information and data in a scientific way; to use methods to increase accuracy of measurements, such as timing over multiple oscillations, or use of a fiduciary marker, set square or plumb line. ## Mathematical Skills There are a number of opportunities for the development of mathematical skills in this unit. These include recognising and making use of appropriate units in calculations; using calculators to handle sin x, cos x, tan x when x is expressed in degrees or radians; finding arithmetic means; identifying uncertainties in measurements and using simple techniques to determine uncertainty when data are combined; translating information between graphical, numerical and algebraic forms; determining the slope and intercept of a linear graph. How Science Works There are opportunities within this topic for learners to use theories, models and ideas to develop scientific explanations; to use appropriate methodology, including ICT, to answer scientific questions and solve scientific problems; to carry out experimental and investigative activities, including appropriate risk management, in a range of contexts; to consider applications and implications of science and evaluate their associated benefits and risks. Learners can investigate the rise and fall of tides and the consequences of resonance. They can consider different methods of preventing vibratory systems resonating and relate this to the design of bridges and the suspension systems of cars. ### Learners should be able to demonstrate and apply their knowledge and understanding of: (a) the definition of simple harmonic motion as a statement in words (b) 2 a x = − as a mathematical defining equation of simple harmonic motion (c) the graphical representation of the variation of acceleration with displacement during simple harmonic motion (d) x A t = + cos( )   as a solution to a = 2 − x (e) the terms frequency, period, amplitude and phase (f) period as 1 f or 2  (g) v A t = − +    sin( ) for the velocity during simple harmonic motion (h) the graphical representation of the changes in displacement and velocity with time during simple harmonic motion (i) the equation 2 m T k =  for the period of a system having stiffness (force per unit extension) k and mass m (j) the equation 2 l T g =  for the period of a simple pendulum (k) the graphical representation of the interchange between kinetic energy and potential energy during undamped simple harmonic motion, and perform simple calculations on energy changes (l) free oscillations and the effect of damping in real systems (m) practical examples of damped oscillations (n) the importance of critical damping in appropriate cases such as vehicle suspensions (o) forced oscillations and resonance, and to describe practical examples (p) the variation of the amplitude of a forced oscillation with driving frequency and that increased damping broadens the resonance curve (q) circumstances when resonance is useful for example, circuit tuning, microwave cooking and other circumstances in which it should be avoided for example, bridge design [[Specified Practical Work]] - Measurement of g with a pendulum - Investigation of the damping of a spring #Component1