A coupled oscillator system consists of two identical masses m and three springs (two outer springs k, one inner spring K connecting the masses). What are the normal mode frequencies for the symmetric and antisymmetric modes?
Correct answer: A. ωsym = √k/m , ωanti = √k+2K/m
- A. ωsym = √k/m , ωanti = √k+2K/m
- B. ωsym = √k+K/m , ωanti = √k/m
- C. ωsym = √2k+K/m , ωanti = √K/m
- D. ωsym = √k/m , ωanti = √2k + K/m
Explanation
In the symmetric mode both masses move together, so only the outer springs (k) affect the motion. In the antisymmetric mode the masses move oppositely, engaging the inner spring K and effectively adding 2K to the restoring force.
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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