Harmonic Oscillator - Modeling and Observations

[squenshl]

Homework Statement

Consider a steel spring with the property that it extends by 10cm (0.1m) in equilibrium when you attach the upper end of the spring to a fixed support and hang a weight of 100g (0.1kg) at the springs lower end.
1) Use the equation for the harmonic oscillator to determine the period of the up and down oscillation you observe when you give the weight a displacement from the equilibrium position by lifting it up and slightly letting it go.
2) Write down different modelling assumptions that you have made by employing these equations.
3) Over what range of amplitude will these equations be valid?
4) Using the same spring, what would you expect to observe when you suspend instead a weight of 1kg?

Homework Equations

The Attempt at a Solution

1) F = kx = mg so k = mg/x = 0.1*9.81/0.1 = 9.81 N/m.
Period T = 2[itex]\pi[/itex]sqrt(m/k) = 2[itex]\pi[/itex]sqrt(0.1/9.81) = 0.63 seconds (2dp).

 

[lippyka]

2) Assumptions: The spring is linear and has a constant rate of restoring force; the spring behaves in a harmonic manner; there is no damping or friction; the applied force is small enough to be considered as a perturbation.3) The equations will be valid for small amplitudes (less than 0.1m).4) We would expect to observe a longer period of oscillation, as the mass is increased from 0.1kg to 1kg. The period can be calculated using the same equation as before, i.e. T = 2\pisqrt(m/k) = 2\pisqrt(1/9.81) = 0.77 seconds (2dp).