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Weighing astronauts
Astronauts need to keep track of their body mass even in the apparent weightless environment of orbit in the space station. They can't use a normal scale. Instead, they step into a chamber attached to a spring of known spring constant k of 12,000 N/m and then vibrate the chamber. A certain astronaut initiates a vibration by displacing the chamber 4 cm from equilibrium. The chamber then vibrates at a frequency of 1.8 Hz. The chamber has a mass of 40 kg. What is hte mass of the astronaut?
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If you keep in mind that w^2 = k/m and w = 2pi*f (f is frequency, m is total mass), then you can solve for the total mass m in terms of f, w, and some constants. However, do not forget to subtract the mass of the chamber from m to get the mass of the astronaut.