![simple harmonic oscillator simple harmonic oscillator](https://sahay.guru/wp-content/uploads/2020/08/Question-no-24_Solution-2-952x1024.jpg)
![simple harmonic oscillator simple harmonic oscillator](https://img.yumpu.com/39800242/1/500x640/1-simple-harmonic-oscillator.jpg)
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
![simple harmonic oscillator simple harmonic oscillator](https://slideplayer.com/slide/8784557/26/images/6/Classical+Harmonic+Oscillator.jpg)
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:
![simple harmonic oscillator simple harmonic oscillator](https://miro.medium.com/max/1200/0*Ds_YEh-eCH-AoJzI.png)
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?