Finding Amplitude of Oscillation for a Spring-Mass System

[05holtel]

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

 

[Dr.D]

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.

 

[Mthees08]

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.

 

[Dr.D]

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.

 

[rl.bhat]

V= -ωAcos(ωt +φ )

This expression is wrong. Check it.