Simple harmonic motion: platform

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SUMMARY

The discussion focuses on a physics problem involving simple harmonic motion (SHM) of a platform with an amplitude of 0.10 m and a frequency of 2.0 Hz. The key conclusion is that the contact between the point mass and the platform will be lost at a height of 62 mm, not at the maximum amplitude of 0.1 m. This occurs because the acceleration of the platform exceeds gravitational acceleration at this point, leading to the loss of contact.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM) principles
  • Familiarity with SHM equations and their applications
  • Knowledge of gravitational acceleration and its effects
  • Basic calculus for analyzing motion and acceleration
NEXT STEPS
  • Study the equations of motion for simple harmonic oscillators
  • Learn about the relationship between frequency, amplitude, and acceleration in SHM
  • Explore the concept of gravitational acceleration and its role in motion
  • Investigate conditions for loss of contact in oscillatory systems
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for examples of SHM applications.

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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.
 
Physics news on Phys.org
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?
 

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