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JJBrian
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Homework Statement
1. A 0.5 kg mass extends a spring 1 cm. What is the frequency of oscillation of this mass
and spring?
2. A 1 m stick is used as a simple pendulum with a 3 kg weight on the end. What is its
period of oscillation?
3. The same meter stick is used as a rigid pendulum with no weight. What is its period?
Homework Equations
F = −kx = ma.
x = Asin(wt) .
w = sqrt(k/m)
w = 2pie/T
v = Awcos(wt) .
vmax= Aw.
a = −A^2sin(wt) .
amax= wvmax=Aw^2.
t = Ia
t = −FLsin(theta) = −mgLsin(theta) = −mgL(theta)
I = mL^2
theta = Asin((2pie/T)*t)
T = 2pie*sqrt(L/g)
2pie/T =sqrt(3g/2L)
The Attempt at a Solution
1. ##w = \sqrt{k/m}##
##w = \sqrt{.01m/.5kg}##
##w = 0.1414~rad/s##
2. ##T = 2\pi~\sqrt{L/g}##
##T = 2\pi~\sqrt{1m/9.8m/s^2}##
##T = 2.007~s##
3. ##2\pi/T = \sqrt{3g/2L}##
##2\pi/T = \sqrt{3(9.8)/2(1)}##
##T = 2\pi/3.834##
##t = 1.6388~s ##
Can someone check my work?
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