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

In summary, the conversation is about finding the amplitude of oscillation for a 200 g ball attached to a spring with a spring constant of 2.40 N/m on a frictionless table. The equations used are f=√(k/m) /2π, x(t) = Acos(2πft), and v(t) = -2πfAsin(2πft). The person initially found that t = 0.137s and A was negative, but then realized that they could ignore the signs and still get the correct answer. They also discussed the significance of the sign of A and how it can switch depending on the choice of solution for t.
  • #1
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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  • #2
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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  • #3
Thanks! I ignored the signs and got the right answer.
 
  • #4
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.
 

1. What is an oscillation problem?

An oscillation problem is a physical phenomenon in which an object moves back and forth repeatedly around its equilibrium position. It is caused by the interplay of restoring forces and energy in a system.

2. How does a horizontal spring affect the oscillation of a ball?

A horizontal spring can act as a restoring force on a ball, causing it to oscillate around its equilibrium position. The stiffness of the spring and the mass of the ball will determine the frequency and amplitude of the oscillation.

3. What factors affect the frequency of oscillation in this problem?

The frequency of oscillation in this problem is affected by the mass of the ball, the stiffness of the spring, and the amplitude of the oscillation. It is also affected by external factors such as air resistance and friction.

4. How is the energy of the system conserved in this oscillation problem?

In this oscillation problem, the energy of the system is conserved because the spring and the ball exchange potential and kinetic energy as they oscillate. The total energy of the system remains constant throughout the oscillation.

5. How can we calculate the period of oscillation in this problem?

The period of oscillation in this problem can be calculated using the formula T = 2π√(m/k), where T is the period, m is the mass of the ball, and k is the spring constant. This formula assumes no external factors such as air resistance or friction.

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