A container crane lifting a container is hit by a gust of wind as it is lifted at t 0.The horizontal displacement (approximately) of the container, y(t), is given bythe equation:yquot;(t) + 2y'(t) + 5y(t) 0;with additional initial conditions rightly or wrongly I solved to:y(3/2)(e^-t)sin(2t)The crane driver can not resume work until the oscillations drop to one tenthof their initial maximum amplitudeHow long must she wait?Does that mean y1/10 and then solve?But with e^-t and a sin(2t) in the function I can't solve for t.Does this mean my solution is wrong, or am I going about it the wrong way?
Trapped? NoLimited options? YesLike any other place, there are a lots of 'options'You have to be realistic when selecting the best one for your pocketbook and circumstance!
The amplitude of the function that you've gotten is (as a function of t) A(t) (3/2) e^(-t) This will be 1/10th the initial maximum when e^(-t) 1/10-i.ewhen t ln(10) You don't have to worry about the sinusoidRemember that the coefficient of the sine function determines the amplitude.
