The velocity and acceleration of a particle performing S.H.M. have a steady phase relationship. The acceleration showed a phase lead over the the velocity of:
Correct answer: B. π/2
- A. π
- B. π/2
- C. -π/2
- D. -π
Explanation
In simple harmonic motion (S.H.M.), the displacement x is given by x = a sin(ωt). The velocity v, being the first derivative of displacement with respect to time, is v = aω cos(ωt). The acceleration a, the derivative of velocity, is given by a = -aω^2 sin(ωt), which can also be expressed as a = aω^2 cos(ωt + π/2). This shows that acceleration leads velocity by a phase of π/2 radians. The other options are incorrect because they represent different or opposite phase relationships that do not apply to the phase relationship between velocity and acceleration in S.H.M.
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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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