Finding Amplitude of Oscillation for a Spring-Mass System

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Homework Help Overview

The discussion revolves around a spring-mass system where a 100 g ball oscillates on a frictionless table. The original poster seeks to determine the amplitude of oscillation given the spring constant and the velocity at a specific position.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply relevant equations for oscillation but expresses uncertainty in solving for amplitude. Some participants suggest revisiting the equations due to a potential differentiation mistake. Others seek clarification on the phase angle, φ, and its role in the equations.

Discussion Status

The discussion is active, with participants providing guidance on the equations and clarifying the meaning of φ. There is an acknowledgment of a possible error in the original poster's expression, prompting further exploration of the problem.

Contextual Notes

Participants are navigating through the implications of the equations and the definitions of variables, particularly the phase angle, which has not been explicitly defined in the context of simple harmonic motion for the spring system.

05holtel
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Homework Statement



A 100 g ball is attached to a spring with spring constant 2.5 N/m oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x = -5.0 cm. What is the amplitude of the oscillation?


Homework Equations



x = Acos(ωt +φ )
V= -ωAcos(ωt +φ )

The Attempt at a Solution



ω = Square root (k/m) = 5 rad/s
-0.05 = Acos(ωt +φ )
0.2 = -ωAcos(ωt +φ )

Not sure how to solve for A
 
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To begin, you need to go back to your (relevant) equations. You have a differentiation mistake there that makes lit impossible to proceed correctly. Get this straight, and the solution for A should become evident using the Pythagorean trig identity.
 
can I get φ clarified is it a constant? I know Acos(ωt+kx) is standard for traveling wave, however I am not certain of SHO for a spring what φ is.
 
When an expression is written in that form, the implication is that phi is the phase angle, a constant. Evidently that was not explicitly stated, and it rarely is, but that is usually what is intended.
 
V= -ωAcos(ωt +φ )

This expression is wrong. Check it.
 

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