Oscillation Problem -- Ball mass on the end of a horizontal spring

[osten]

Homework Statement

A 200 g ball attached to a spring with spring constant 2.40 N/m oscillates horizontally on a frictionless table. Its velocity is 20.0 cm/s when x=−5.00cm.
What is the amplitude of oscillation?

Homework Equations

f=√(k/m) /2π
x(t) = Acos(2πft)
v(t) = -2πfAsin(2πft)

The Attempt at a Solution

I found that t = 0.137s, and A turned out to be negative, so it was probably wrong.

 

[haruspex]

I found that t = 0.137s, and A turned out to be negative, so it was probably wrong.

You do not show your working, but there should be multiple solutions for t. Some will produce a positive A and some negative. What do you conclude from that?

 

[osten]

Thanks! I ignored the signs and got the right answer.

 

[haruspex]

Thanks! I ignored the signs and got the right answer.

Good. Do you understand why the choice of solution for t can switch the sign?
By the way, you did not need to find t at all. You could have used sin²+cos²=1.