Factors Affecting the Time Period for Oscillations in a Mass-spring System

Factors Affecting the Time Period for Oscillations in a Mass-spring System

When a mass is attached to the end of a spring the downward force the

mass applies on the spring will cause the spring to extend. We know

from Hooke's law that the force exerted by the masses attached to the

spring will be proportional to the amount the spring extends. F = kx

When additional downward force is applied to the spring we can cause

additional tension in the spring which, when released, causes the

system to oscillate about a fixed equilibrium point. This is related

to the law of conservation of energy. The stain energy in the spring

is released as kinetic energy causing the mass to accelerate upwards.

The acceleration due to gravity acting in the opposite direction is

used as a restoring force which displaces the mass as far vertically

as the initial amplitude applied to the system and the process

continues.

A formula that can be used to relate mass applied to a spring system

and time period for oscillations of the system is

T = 2π√M/k

This tells us T2 is proportional to the mass

To test this relationship an experiment will have to be performed

where the time period for an oscillation of a spring system is related

to the mass applied to the end of the spring.

Variables that could affect T

Mass applied to spring; Preliminary experiments should be performed to

assess suitable sizes of masses and intervals between different masses

used in the experiment.

Spring constant; The spring constant will be useful to confirm the

relationship. A simple force - extension experiment should be

performed to get an accurate value for k which can be compared to the

value of k from the final experiment.

Amplitude; The amplitude of the oscillations should be kept constant.

Bear in mind the amplitude cannot be larger than the extension caused

by the smallest mass applied to the spring as this would not allow the

system to oscillate properly.