How Do You Calculate the Amplitude of Oscillation for a Spring-Mass System?

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SUMMARY

The amplitude of oscillation for a spring-mass system can be calculated using the formula A = v(t) / (\omega * sin(\omega t)), where \omega is derived from the spring constant and mass. In this case, with a spring constant of 2.50 N/m and a mass of 200 g, \omega is calculated to be 3.54 rad/s. The amplitude is determined to be 5.09 cm. For part B, the speed of the ball when x = 3.00 cm is found to be 14.56 cm/s, although the original poster expressed confusion regarding the correctness of these answers.

PREREQUISITES
  • Understanding of harmonic motion principles
  • Familiarity with spring constant calculations
  • Knowledge of angular frequency (\omega) in oscillatory systems
  • Basic proficiency in trigonometric functions and their applications in physics
NEXT STEPS
  • Review the conservation of energy in spring-mass systems
  • Study the derivation of angular frequency (\omega) in oscillatory motion
  • Practice solving problems involving potential energy of springs
  • Explore the relationship between displacement and velocity in harmonic motion
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Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to clarify concepts related to spring-mass systems.

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Homework Statement


A 200 g ball attached to a spring with spring constant
2.50 N/m oscillates horizontally on a frictionless table. Its velocity is 18.0 cm/s when x = -5.00 cm.
A. What is the amplitude of oscillation?

B. What is the speed of the ball when x = 3.00 cm?

Homework Equations


A. [tex]\omega[/tex] = sqrt k/m = sqrt 2.50/.200
v(t) = A*[tex]\omega[/tex]*sin([tex]\omega[/tex]t)
t = 0
v(t) = A[tex]\omega[/tex]

B. Vx2 = [tex]\omega[/tex]2(A2 - x2)

The Attempt at a Solution


I've tried several times to get a solution and I have never gotten the same answer twice...
A. [tex]\omega[/tex] = 3.54
A = 5.09 cm

B. When x = 3.00 cm, V = 14. 56 cm.

Neither of these answers are correct and I'm not sure what I am doing wrong. I am doing everything as explained to me in class. I'm so confused...
 
Last edited:
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Have you been taught about conservation of energy, and the potential energy of a spring?

Also, is there supposed to be a question in part A? I only see a question in B.
 

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