Simple harmonic motion: platform

[Kushal]

Homework Statement

A point mass rests on a horizontal platform which can be made to describe vertical s.h.m. of amplitude 0.10m and frequency 2.0 Hz. The mass makes contact with the platform as it rises from its lowest point. At what point, if any, will this contact be lost?

Homework Equations

shm equations

The Attempt at a Solution

i'm thinking that this will happen at the top, x = 0.1 m, where after instantaneous zero velocity, the platform will be attracted to a larger extent downwards than the particle. but then the answer is x = 62 mm. i don't understand.

 

[Kurdt]

For this problem you will have to find the point where the harmonic oscillator accelerates faster than the acceleration due to gravity. What do you know about SHM and acceleration?

 

[m2003]

I would first clarify the given information and make sure that all the necessary variables are accounted for. For example, is the platform undergoing simple harmonic motion in the vertical direction while the point mass remains stationary? Or is the point mass also undergoing simple harmonic motion along with the platform? This information would affect the equations and solution.

Assuming that the platform is undergoing simple harmonic motion in the vertical direction while the point mass remains stationary, the contact between the mass and platform will be lost at the point where the platform's acceleration is equal to the acceleration due to gravity. This can be determined using the equation for simple harmonic motion: a = -ω²x, where ω is the angular frequency (2πf) and x is the displacement from equilibrium.

At the top of the platform's motion (x = 0.1m), the acceleration of the platform is equal to ω²x = 2π²(2.0 Hz)²(0.1m) = 2.5 m/s². This is greater than the acceleration due to gravity (9.8 m/s²), so the platform will continue to accelerate downwards while the mass remains stationary. Therefore, the contact will be lost at the top of the platform's motion.

I'm not sure where the given answer of x = 62 mm comes from, as it is not a clear solution without knowing the context of the problem. As a scientist, it is important to always double check calculations and make sure they are consistent with the given information and equations.