Finding Amplitude of Oscillation for a Spring-Mass System

AI Thread Summary
To find the amplitude of oscillation for a spring-mass system, the equations x = Acos(ωt + φ) and V = -ωAcos(ωt + φ) are relevant. The angular frequency ω is calculated as 5 rad/s based on the spring constant and mass. The values for position and velocity at a specific time lead to a system of equations that can be solved for amplitude A. Clarification on the phase angle φ indicates it is a constant, typically not explicitly stated in such problems. Correcting any differentiation mistakes is essential for accurately determining the amplitude.
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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