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.
Why is simple harmonic motion so important?