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Unformatted text preview: %. Does linear approximation say anything meaningful about the change in ux when the radius changes from 1mm to 3mm? 3. A pendulum is swinging from side to side. At time t , the angle between the pendulum and a vertical line is ( t ). It is known that ( t ) satises the dierential equation 00 ( t ) =-sin( ( t )) . 1. This equation is too hard to solve. Use linearization to approximate the right hand side when ( t ) is very small. 2. Replace the right hand side with the linear approximation you found. Show that ( t ) = C cos( t ) is a solution to the new dierential equation, where C is a constant. 2...
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