A quick Physics 2 homework question !!

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1

<p>Hey guys, I think I got parts b and c of this question, but I'm totally confused on part a.) ... I think they want a derivation ... how do I do that?</p>

<p>Designed for use on orbiting space vehicles is the following device whose purpose is
to allow astronauts to measure their mass under weightless conditions. The device is
a spring mounted chair; an astronaut measures his or her period of oscillation in the
chair; the mass follows from the formula for the period of an oscillating mass-spring
system.
a) If M is the mass of the astronaut and m the effective mass of that part of the
device that also oscillates, show that
M = (T^2)(k)/(4pi^2) - m,
where T is the period of oscillation and k is the spring constant.</p>

2

<p>Here is what I've tried so far:</p>

<p>T = (2pi) / sqrt(k/M)</p>

<p>T^2 = (4pi^2) / (k/M)</p>

<p>T^2 = (4pi^2)(M) / (k)</p>

<p>(T^2)k = (4pi^2)M</p>

<p>M = (T^2)(k) / (4pi^2)</p>

<p>Two questions:
1.) in the 5 steps above, did I correctly use big M (should I be using "M" like I did, or "m")?</p>

<p>2.) how do I make it say " - m " at the end? Can you just add that " - m" in at the end, or should that be somehow derived too?</p>

3

<p>You should have used M+m instead of M, as both the astronaut and the device are oscillating.</p>

4

<p>Thanks man. It works now :-)</p>