A horizontal plank is executing SHM along the vertical...

A horizontal plank is executing SHM along the vertical direction with angular frequency $\omega .$ A coin is placed on top of this plank. If the amplitude of oscillation is increased gradually, for what maximum amplitude will the coin be on the verge of loosing contact with the plank? (A) When is plank is at its maximum height (B) When the plank is at the midpoint. (C) When the amplitude is $\left(\mathrm{g} / \omega^{2}\right)$ (D) When the amplitude is $\left(\mathrm{g}^{2} / \omega^{2}\right)$

A horizontal plank is executing SHM along the vertical direction with angular frequency $\omega .$ A coin is placed on top of this plank. If the amplitude of oscillation is increased gradually, for what maximum amplitude will the coin be on the verge of loosing contact with the plank?
(A) When is plank is at its maximum height
(B) When the plank is at the midpoint.
(C) When the amplitude is $\left(\mathrm{g} / \omega^{2}\right)$
(D) When the amplitude is $\left(\mathrm{g}^{2} / \omega^{2}\right)$

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Key Concepts

Normal Force and Conditions for Loss of Contact

The normal force is the contact force exerted by a surface to support the weight of an object. When an object is on an oscillating platform, it will lose contact if the acceleration of the platform exceeds or equals the acceleration due to gravity. Specifically, for a platform in SHM, the object is on the verge of losing contact when A?² equals the gravitational acceleration g.

Simple Harmonic Motion

SHM is a type of periodic motion where an object oscillates about an equilibrium position with a restoring force that is directly proportional to its displacement. It is characterized by parameters such as amplitude, angular frequency, and phase, and the position and acceleration of the object vary sinusoidally with time.

Maximum Acceleration in SHM

In SHM, the maximum magnitude of the acceleration is given by the product of the amplitude and the square of the angular frequency (A?²). This maximum acceleration occurs when the object is at its extreme position in the motion. It is a key concept when analyzing the dynamic forces acting on objects in oscillatory systems.

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