- #1
Kizaru
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Homework Statement
An object of unknown mass M is hung from a vertical spring of unknown spring constant k, and the object is observed to be at rest when the spring has extended by 14cm. The object is then given a slight push and executes SHM. Determine the period of this oscillation.
Homework Equations
T = 1/f
w = (k/M)^(1/2) = 2pi*f
F=kx
The Attempt at a Solution
The object is hanging, so it has a force of Mg pulling it down and kx pulling it up. It's in equilibrium at a displacement of 14cm (0.14m). So I set kx = Mg and solved for k:
k = Mg / x
I then plugged this into w = (k/M)^(1/2) so the M's cancel and I'm left with w = (g/x)^(1/2) = (9.8 / 0.14)^(1/2) = 70rad/s
w = 2pi*f => f = w/(2pi) = 11.14 Hz
T = 1/f = 0.089s
This isn't the right answer according to the book, and I keep getting this kind of problem wrong. I'm not entirely sure what I'm doing wrong.