- #1
Becca93
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Homework Statement
Damping is negligible for a 0.139 kg mass hanging from a light 7.00 N/m spring. The system is driven by a force oscillating with an amplitude of 1.88 N. At what frequency will the force make the mass vibrate with an amplitude of 0.430 m? There are two possible solutions, enter one of them.
Homework Equations
A = (Fo/m) / (√((ω^2 - ωo^2)^2 + (bω/m)^2)
Damping is negligible, therefore b = 0, therefore
A = (Fo/m) / (√((ω^2 - ωo^2)^2)
ωo = √(k/m)
The Attempt at a Solution
So,
m = 0.139 kg
k = 7.00 N/m
Fo = 1.88 N
A = 0.430 m
A = (Fo/m) / (√((ω^2 - ωo^2)^2)
Rearranged to find ω, is
(ω^2 - √(k/m)^2)^2 = (Fo/m) / A
ω^2 = √((Fo/m)/A) + (k/m)
ω = √( √((Fo/m)/A) + (k/m) )
So,
ω = √( √((1.88/0.139)/0.430) + (7/0.139) )
ω = √( 1.77 + 50.3597)
ω = 7.22 rad/s
ω = 2(pi)f
7.22 /2(pi) = f
f = 1.49 Hz
This is not the correct answer and I have no idea where I'm going wrong.
Am I using the wrong equations? Are my calculations incorrect? Any assistance would be much appreciated.