Strings and springs

• The tension in a stretched (or compressed) string or spring is T = $\lambda$ x/l.
• The natural length, l, of a string or spring is the length when there is no force on it.
• The modulus of elasticity, $\lambda$ , is a measure of how stiff a string or spring is. The greater the modulus of elasticity, the less stretchy the string or spring is.
• Hooke's law only applies for values of extension, x, up to the elastic limit.
• When in equilibrium, the components of tension on each string/spring must be equal.
• Elastic potential energy stored in a stretched string/spring is the amount of work done in stretching the string/spring and is E = $\lambda$ x^2/2l.
• For a string/spring, energy must be conserved in terms of elastic potential energy as well as kinetic and potential energy.