# Harmonic oscillator question

1. Apr 12, 2012

### squenshl

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

3. 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$\pi$sqrt(m/k) = 2$\pi$sqrt(0.1/9.81) = 0.63 seconds (2dp).