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

AI Thread Summary
A 200 g ball attached to a spring with a spring constant of 2.40 N/m oscillates on a frictionless table, with a velocity of 20.0 cm/s at x = -5.00 cm. The amplitude of oscillation was initially calculated incorrectly, resulting in a negative value. It was clarified that multiple solutions for time (t) exist, which can lead to both positive and negative amplitude results. The discussion noted that the sign of the amplitude can be adjusted by choosing different solutions for t, and that finding t was unnecessary for solving the problem. The correct approach involves using the relationship sin² + cos² = 1 to determine the amplitude.
osten
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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.
 
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osten said:
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?
 
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Thanks! I ignored the signs and got the right answer.
 
osten said:
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.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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