Prove that motion is simple harmonic when given an equation of motion for acceleration, velocity or displacement and describe the resulting motion. Derive equations for displacement, velocity and acceleration in terms of time, given that a motion is simple harmonic and describe the motion modelled by these equations. Year 12 Mathematics Extension 2: Simple Harmonic Motion NESA Syllabus Outcomes Another notable research project is the work of the Birmingham Solar Oscillation Network (BiSON), who focus on measuring oscillations in the sun (helioseismology) and nearby stars (astroseismology) to learn about their internal structures.We take your privacy seriously. There the detectors are so sensitive that careful modelling and minimisation of the surrounding vibrations and noise are crucial. At the University of Birmingham, one of the research projects we have been involved in is the detection of gravitational waves at the Laser Interferometer Gravitational-Wave Observatory (LIGO). Simple harmonic motion is important in research to model oscillations for example in wind turbines and vibrations in car suspensions. Whilst simple harmonic motion is a simplification, it is still a very good approximation. This means that effects such as damping, which acts to reduce the amplitude by removing energy from the system, are a good example of where simple harmonic motion contributes to improving our day-to-day lives. The vibrations and oscillations that surround us in our everyday lives are generally much more complicated than those we encounter in simple harmonic motion. In this episode we look at generating and measuring waves and the use of appropriate digital instruments. In the Laboratory Confessions podcast researchers talk about their laboratory experiences in the context of A Level practical assessments. Assuming simple harmonic motion, the periodic nature of these systems mean that there should be no excuse when it comes to taking multiple measurements! Laboratory Confessions It can also be useful to use a pin or tag to act as a fiduciary marker showing the equilibrium position. To obtain more accurate measurements of the spring constant and the gravitational acceleration, repeated measurements should be taken using various pendulum lengths and masses.Īlso, measuring period over a longer time frame (and hence over multiple oscillations) will increase the accuracy since the human error will be a smaller fraction of the recorded time. To improve the accuracy on the period, the timings can be taken over multiple oscillations and by averaging over several measurements of the period. If a body moves in such a way that its acceleration is directed towards a fixed point in its path and directly proportional to the distance from that point, the movement of the object is said to be simple harmonic. In this experiment one of the major sources of error is down to the human reaction time when measuring the period. Definition of Simple Harmonic Motion - SHM. The experiments described here demonstrate the use of a mix of analogue and digital apparatus to measure quantities including mass, length and time. The period of a simple harmonic oscillator is also independent of its amplitude.įrom its definition, the acceleration, a, of an object in simple harmonic motion is proportional to its displacement, x: Note that in the case of the pendulum, the period is independent of the mass, whilst the case of the mass on a spring, the period is independent of the length of spring. 
Described by: T = 2π√(m/k).īy timing the duration of one complete oscillation we can determine the period and hence the frequency.
Mass on a spring - Where a mass m attached to a spring with spring constant k, will oscillate with a period ( T). Described by: T = 2π√(l/g), where g is the gravitational acceleration.Ģ. Pendulum - Where a mass m attached to the end of a pendulum of length l, will oscillate with a period ( T). The two most common experiments that demonstrate this are:ġ. Since simple harmonic motion is a periodic oscillation, we can measure its period (the time it takes for one oscillation) and therefore determine its frequency (the number of oscillations per unit time, or the inverse of the period). Simple harmonic motion is a very important type of periodic oscillation where the acceleration ( α) is proportional to the displacement ( x) from equilibrium, in the direction of the equilibrium position. Oscillations are happening all around us, from the beating of the human heart, to the vibrating atoms that make up everything. Why is simple harmonic motion so important?
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