Consider the graph shown for the position of a ball attached to a spring as it oscillates in simple harmonic motion. Which of the following is correct?
The speed of ball is greatest at 2s
(ii)The speed of ball is greatestat 4s
(iii)The acceleration of ball is greatest at 2s
(iv)The acceleration of ball is greatest at 6s

Answer

B

Explanation

For a simple harmonic motion, `x=Asinomegat` . The speed is given by `f=(dx)/(dt)=AomegatRightarrow f_(max)=01`Thus, the speed is greatest when the amplitude is 0, so it is greatest at . The acceleration is given by
`a=(dx)/(dt)=-Aomega^(2)sinomegatRightarrowa_(max)=-Aomega^(2)`
Thus, the acceleration would be maximum when the amplitude is greatest, so it is maximum at 2s and 6s.