5133 A ball on a spring is pulled 2 inches below its rest po

5.133 A ball on a spring is pulled 2 inches below its rest position and then released. After Find all values of t for which the ball is 1 inches above its rest position. Give a general formula for all the solutions by adding multiples of some positive integ Type your answer in radians. Use integers or fractions for any numbers in the expres En the answer box and then click Check Ans

Solution

d =-2cos((_/3)t)

1 inch above rest position. => d =1

=>-2cos((_/3)t)=1

=>cos((_/3)t)=-1_/2

=>((_/3)t) =2n -(2_/3) ,2n +(2_/3)

=>t =(3_/)(2n -(2_/3)) ,(3_/)(2n +(2_/3))

=>t =6n -2 ,6n+2 where n is an integer