The net x -force on a 1-kg oscillating object moving along the x axis is F x = ?

Question

The net x-force on a 1-kg oscillating object moving along the x axis is Fx = ?b(x ? a2x3), where b = 130 and a = 3 with the appropriate SI units.

(b) What is the frequency of such small oscillations? Include 2 decimal places.

So far I think that our k s  will be equal to -130, because at significantly small vales the a2x3 will be equal to 0,        

The net x-force on a 1-kg oscillating object moving along the x axis is Fx = ?b(x ? a2x3), where b = 130 and a = 3 with the appropriate SI units. For small oscillations, this force law reduces to the harmonic oscillator law F x ?k sx, where ks depends on the value of a and/or b. (b) What is the frequency of such small oscillations? Include 2 decimal places. So far I think that our k s will be equal to -130, because at significantly small vales the a2x3 will be equal to 0, making our F x -130x. If this is the case how do you solve for the frequency?

Explanation / Answer

m*w^2*x = Fx, where m is mass; w is angular frequency and x is oscillation distance

In small oscillations, Fx =~ -130x

Thus, w = sqrt(Fx/(m*x)) = 11.4 rad/s

Thus frequency, f =w/(2*pi) = 1.815 Hz

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