A wire could be shaped like a sinusoidal function and then we could say the bead moves harmonically.(adsbygoogle = window.adsbygoogle || []).push({});

The shape of the wire, so that bead occilates around X = 0.

Y = -50*cos(10X)

If we ignore friction and give it a small dispalcement then it is possible to find angular frequency.

However, when I applied my method to a varation of this problem in a text book I got a wrong answer.

Part I:

Here was my attempt where Z is the angle from the center of the circle that the bottom of the sinudosoidal function fits on:

S = (r)*(Z) = (50)*(Zmax sin wt)

V= 50*Zmax*w*coswt

V(max) = 50*Zmax*w

Part II:

Energy at the lowest place

E = .5 m (Vmax)^2 - 50mg

Energy at the highest place

E = -50mg*cos(Zmax)

Setting the energies equal:

.5 m (Vmax)^2 - 50g =-50mg*cos(Zmax)

Solving for the velocity:

(Vmax)^2 = 100g*[1-cos(Zmax)]

Part III: combing part I & II

(Vmax)^2 = 100g*cos(Zmax)

(50*Zmax*w)^2 = 100g*[1-cos(Zmax)]

library logged me off, i will finish later

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# Homework Help: Bead on a Wire and Harmonic Motion

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