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. In this experiment one of the major sources of error is down to the human reaction time when measuring the period. 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. If the net force can be described by Hooke’s law and there is no damping (by friction or other non-conservative forces), then a simple harmonic oscillator will oscillate with equal displacement on either side of the equilibrium position, as shown for an object on a spring in Figure 16.9.Why is simple harmonic motion so important? Simple Harmonic Motion (SHM) is the name given to oscillatory motion for a system where the net force can be described by Hooke’s law, and such a system is called a simple harmonic oscillator. They are also the simplest oscillatory systems. The oscillations of a system in which the net force can be described by Hooke’s law are of special importance, because they are very common. 6.B.1.1 The student is able to use a graphical representation of a periodic mechanical wave (position versus time) to determine the period and frequency of the wave and describe how a change in the frequency would modify features of the representation.6.A.3.1 The student is able to use graphical representation of a periodic mechanical wave to determine the amplitude of the wave.3.B.3.4 The student is able to construct a qualitative and/or a quantitative explanation of oscillatory behavior given evidence of a restoring force.3.B.3.1 The student is able to predict which properties determine the motion of a simple harmonic oscillator and what the dependence of the motion is on those properties.The information presented in this section supports the following AP® learning objectives and science practices: Relate physical characteristics of a vibrating system to aspects of simple harmonic motion and any resulting waves.By the end of this section, you will be able to do the following:
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