Platform on Springs: Find Effective Spring Constant & Oscillation Amplitude

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Homework Help Overview

The problem involves a platform supported by springs and a mass of modeling clay that impacts the platform, causing it to oscillate. The subject area includes mechanics, specifically concepts related to spring constants and oscillatory motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the effective spring constant and the net displacement of the springs. Questions arise regarding the forces involved in the compression of the springs and the conservation of momentum during the collision.

Discussion Status

Some participants are exploring the relationship between force and displacement to determine the effective spring constant. Others are considering the implications of momentum conservation in the context of the collision between the clay and the platform.

Contextual Notes

There is a focus on the instantaneous nature of the collision and the resulting oscillation of the platform. The problem setup includes specific masses and a defined displacement, which may influence the calculations and assumptions made by participants.

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A platform of mass 0.8 kg is supported on four springs (only two springs are shown in the picture, but there are four altogether). A chunk of modeling clay of mass 0.6 kg is held above the table and dropped so that it hits the table with a speed of v = 0.9 m/s.

The clay sticks to the table so that the the table and clay oscillate up and down together. Finally, the table comes to rest 6 cm below its original position.


a) What is the effective spring constant of all four springs taken together?

b) With what amplitude does the platform oscillate immediately after the clay hits the platform?
 
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Can you show us what work and/or ideas you have put forth so far?
 
a) What is the net displacement Delta x of the spring from its former equilibrium position? What force F was required to compress the springs? The effective spring constant is the ratio F/(delta x).
 
The first thing in this problem is a conservtion of momentum. Assume the collision is instantaneous, so there are no net forces to worry about. What will be the velocity of the clay/platform combination immediately after collision?
 

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