A very sensitive spring balance consists of a quartz spring suspended vertically from a fixed support. The spring constant is k. The balance is at temperature T in a location where the gravitational acceleration is g.
(a) When a small object of mass m is suspended from the spring, the spring will be stretched out by an amount x and will reach an equilibrium position. However, thermal energy will cause fluctuations in x. Ignoring the mass of the spring, what is the average value of x, ?
(b) What is the magnitude of thermal fluctuations of the object, <(x-)2>1/2 ?
(c) When the fluctuations become comparable to the average value, the measurement becomes impractical. How small mass can this balance measure?