# The Two Properties Of The Mass Spring System

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The higher the mass leads to a slower vibration. Any physical object, whether it be air or a spring which both have spring like stiffness and inert mass have vibratory properties. An increase in mass increases the inertia of the object. Increased inertia means that the springs will not be able to make the mass change direction as quickly. This increases the time period of the oscillation. The greater the inertia of an oscillating object, the greater the time period which therefore lowers the frequency of its oscillations. Depending on how the waves are displaced indicates how big the oscillations.

The elasticity of a spring also can be quantified by a measure of a spring’s compliance. Compliance is inversely related to stiffness, which means that springs that have relatively little stiffness are characterised by a relatively large compliance. As compliance increases, the force required to compress or stretch the spring decreases. Hence, compliant springs can be displaced from equilibrium more easily than stiff springs. If the mass is moved to the right and then released, the system will be set into vibration. When the restoring force of elasticity overcomes the inertial force, the direction

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Molecules are displaced from their resting position. Air pressure increases above its resting pressure because the molecules are being compressed. Because air is an elastic medium the particles displace in the opposite direction. The rebounding air molecules accelerate due to mass effects and the further the air molecules move outwards, air pressure is reduced below atmospheric pressure known as rarefaction. The air molecule will vibrate back and forth, thus simple harmonic motion of the first air molecule is transmitted to the one next to it. The second one similarly initiates vibration of the one to its right and so forth down the line. Any vibrating system for which the magnitude of the restoring force Fr is directly proportional to the displacement x can be described as simple harmonic or sinusoidal motion. Simple Harmonic Motion can be illustrated as uniform circular motion. The to and fro vibration of a mass on a spring or air molecules is analogous to a point moving around the circumference of a circle at a constant rate.

During the course of oscillation, the magnitude of restoring force changes over time because magnitude of displacement changes. As mass moves towards equilibrium Fr reduces, as mass moves away from equilibrium, maximum displacement, Fr