For a vibrating mass-spring system, the expression of kinetic energy if x=0 is given by:
Correct answer: B. B
- A. A
- B. B
- C. C
- D. D
Explanation
In a mass-spring system, the kinetic energy is given by the formula: KE = ½ mv²In the case of a vibrating mass-spring system, the maximum displacement from equilibrium position (amplitude) is denoted by xo. At the equilibrium position (x = 0), the velocity is maximum, and it can be calculated as: v = ωxoWhere ω is the angular frequency. Now, substituting the values into the formula for kinetic energy, we have:KE = (½)m(ωxo)²= ½ mω²xo²Since k is the spring constant and: k = mω²We can rewrite the equation as: KE = ½ kxo²
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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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