(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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)

3. 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.

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# Homework Help: Forced Oscillator where Damping is Negligible

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