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Yes, my remark about t=0 was only in relation to part c.JulienB said:
For part b, the only other suggestion I have is that it should say to find αR in terms of m, L, k and x0.
Spring and string pendulum (oscillations)
- Thread starter JulienB
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- Oscillations Pendulum Spring String
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SUMMARY
The discussion revolves around the dynamics of a pendulum influenced by a spring, specifically focusing on the equation of motion for small angles (α << 1). The equation derived is α'' + (k/m)⋅α = 0, leading to the angular frequency ω = √(3k/m) and the equilibrium angle αR = 2⋅B. Participants clarify the initial conditions and the role of gravity, ultimately arriving at the corrected equation of motion α'' + ((g/L) + (k/m))⋅α = 0, which incorporates gravitational effects. The conversation highlights the importance of accurately interpreting initial conditions and forces acting on the pendulum.
PREREQUISITES- Understanding of simple harmonic motion (SHM)
- Familiarity with pendulum dynamics and torque
- Knowledge of spring mechanics and Hooke's Law
- Basic calculus for solving differential equations
- Study the derivation of equations of motion for coupled oscillators
- Explore the effects of damping in oscillatory systems
- Learn about the small angle approximation in pendulum motion
- Investigate the role of initial conditions in dynamic systems
Students and educators in physics, mechanical engineers, and anyone interested in the dynamics of oscillatory systems, particularly those involving springs and pendulums.
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