- #31
Maximizing Displacements in SHM: Is ωt = -Φ/2 the Correct Value?
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SUMMARY
The forum discussion centers on the maximum displacement between two particles in simple harmonic motion (SHM) described by the equations y1 = Asin(ωt) and y2 = Asin(ωt+Φ). The maximum displacement is calculated to be 3A/2, occurring when ωt = -Φ/2. However, participants debate the correctness of this value due to the resulting opposite signs in displacements, which contradicts the expected behavior of the system. Ultimately, the correct phase angle Φ is derived as sin-1(3√7/8), leading to the conclusion that the maximum displacement is A(√7/4).
PREREQUISITES- Understanding of simple harmonic motion (SHM)
- Familiarity with trigonometric identities and inverse functions
- Knowledge of phase angles in oscillatory systems
- Ability to manipulate and solve equations involving sine and cosine functions
- Study the derivation of maximum displacement in SHM using trigonometric identities
- Learn about the implications of phase differences in oscillatory motion
- Explore the use of inverse trigonometric functions in solving SHM problems
- Investigate the effects of varying amplitude and phase on the behavior of coupled oscillators
Students studying physics, particularly those focusing on mechanics and oscillations, as well as educators seeking to clarify concepts related to simple harmonic motion and phase relationships.
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