Explanation Given information: Frequency x m = 6 Η z Maximum velocity v = 4 f t / s The equation of a simple harmonic motion is given as: x = x m sin ( ω n t + ϕ ) We can obtain the velocity (v) at any time (t) by differentiating (x) with respect to (t), Since, v = d x d t v = d d t ( x m sin ( ω n t + ϕ ) ) v = ω n x m cos ( ω n t + ϕ ) The acceleration (a) can be obtained by differentiating again the above equation with respect to (t), a = d v d t a = d d t ( ω n x m cos ( ω n t + ϕ ) ) a = − ω n 2 x m sin ( ω n t + ϕ ) Since the particle moves in simple harmonic motion with maximum velocity is, v = ω n x m Also, the maximum acceleration is, a = ω n 2 x m Calculation: Frequency: f n = ω n 2 π 6 = ω n 2 × 3

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Chapter 19.1, Problem 19.3P

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The amplitude and maximum acceleration of a particle in simple harmonic motion.

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The amplitude and maximum acceleration of a particle in simple harmonic motion.

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