What is the phase of the SHM at that point

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SUMMARY

The discussion focuses on a mass-spring system undergoing simple harmonic motion (SHM). The mass is initially stretched by 0.1 m and released, achieving a speed of 1 m/s at the equilibrium position. The speed of the mass when compressed by 0.05 m is calculated to be 0.866 m/s using the formula V = ω √(A² - y²), where ω is determined to be 10 rad/s. The phase of the SHM at the compression point is established as 120°, derived from the relationship of the amplitude and cosine function in SHM.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Familiarity with the mass-spring system dynamics
  • Knowledge of angular frequency (ω) and its calculation
  • Ability to apply trigonometric functions in the context of SHM
NEXT STEPS
  • Study the derivation of the SHM equations, focusing on V = ω √(A² - y²)
  • Learn about the relationship between phase angle and position in SHM
  • Explore the implications of amplitude and frequency on SHM behavior
  • Investigate energy conservation in mass-spring systems during SHM
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Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators looking for examples of SHM applications.

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Homework Statement



A mass is attached to a spring on a frictionless horizontal surface. The mass is pulled to stretch the spring by 0.1 m, & then gently released. A short time later, as the mass passes through the equilibrium position, its speed is 1 m/s.

Part a)

What is the speed of the mass at the point where the spring is compressed by 0.05 m?

Part b)

What is the phase of the SHM at that point, relative to a phase of zero at the time of release?

Homework Equations



The Attempt at a Solution



Part a)

A = 0.1 m
ωA =1 m/s
ω = 1 / 0.1 = 10 rad/s
y = 0.05 m
V = ω √ (A2 - y2)
= 10 * [ √ ( 0.01 - 0.0025 ) ]
= 0.866 m/s, this answer is correct because my teacher gave us the answer.

Part b)

Answer = 120°, how to get this answer?
 
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Hi Voltrical! :smile:
Voltrical said:
Part b)

Answer = 120°, how to get this answer?

shm is amplitude times cosωt …

so won't it have something to do with cos120° ? :wink:
 

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