Question
The vertical motion of a huge piston having a small block of mass m placed over it in simple harmonic motion with a frequency is ω . What is the maximum amplitude of piston’s simple harmonic motion for block and piston to remain together?
Solution
If the acceleration of piston is less or equal to acceleration due to gravity at that point, the block will not leave the piston at any point.
The value equal to 'g' for the block not to leave the piston is the maximum acceleration at the extreme point.
Therefore,
where A is amplitude of vibration.
