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## Homework Statement

A 10lb bar is pinned at its center O and connected to a torsional spring. The spring has a stiffness k = 5 lb ft/rad so that the torque develped is M = 5(theta) lb ft where theta is in radians. If the bar is released from rest when it is vertical at theta = 90 degrees, determine its angular velocity at the instand theta = 45 degrees

## Homework Equations

I(o) = .5mr^2

Moment = I(o)a where a is angular acceleration

w^2 = w(o)^2 + 2a(theta - theta(initial))

## The Attempt at a Solution

10lb = .3108 slug

I = .5(.3108)(1^2) = 1.554 sluf ft^2

Moment = Ia 5theta = 1.554a

a = 32.1750theta

90 degrees = 1.5708 radians

45 degrees = .7854 radians

w^2 = 0 + 2(32.1750)(.7854)(.7854 - 1.5708)

w = 6.3004 rad/s

Should the inital theta be 0.