- #1
Saitama
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Homework Statement
An astronaut in the International Space-station attaches himself to the four vertices of a regular tetrahedron shaped frame with 4 springs. The mass of the springs and their rest length are negligible, their spring constants are ##D_1=150 N/m##, ##D_2=250 N/m##, ##D_3=300 N/m## and ##D_4=400 N/m##. For the sake of simplicity - the astronaut is considered pointlike, its mass is m=70 kg. What is the period of the oscillation of the astronaut if he is displaced from his equilibrium position and released?
Homework Equations
The Attempt at a Solution
I haven't yet attempted the problem by writing down the equations when the astronaut is displaced from centre because looking at the answer given, I think there is a shorter way. The given answer is
$$2\pi \sqrt{\frac{m}{D_1+D_2+D_3+D_4}}$$
If it is a coincidence, I am ready to make the equations.
Any help is appreciated. Thanks!