As an aid in working this problem, consult Concept Simulation 10.3 . A block of

Question

As an aid in working this problem, consult Concept Simulation 10.3.

A block of mass m = 0.685 kg isfastened to an unstrained horizontal spring whose spring constantis k = 86.5 N/m. The block isgiven a displacement of +0.120 m, where the + sign indicates thatthe displacement is along the +x axis, and then releasedfrom rest. (a) What is the force (magnitude and direction)that the spring exerts on the block just before the block isreleased?
1 N

(b) Find the angular frequency of the resultingoscillary motion.
2 rad/s

(c) What is the maximum speed of the block?
3 m/s

(d) Determine the magnitude of the maximum acceleration of theblock.
4 m/s2

Section 10.2 Simple Harmonic Motion and TheReference Circle (a) What is the force (magnitude and direction)that the spring exerts on the block just before the block isreleased?
1 N

(b) Find the angular frequency of the resultingoscillary motion.
2 rad/s

(c) What is the maximum speed of the block?
3 m/s

(d) Determine the magnitude of the maximum acceleration of theblock.
4 m/s2
Section 10.2 Simple Harmonic Motion and TheReference Circle

Explanation / Answer

mass m = 0.685 kg sprimg constant k = 86.5 n / m amplitude A = 0.12 m (a). the force (magnitude and direction) that the springexerts on the block just before the block is released = -Ak                                                                                                                                                                 = -10.38 N it is along negative X - axis (b). the angular frequency of the resultingoscillary motion = [ k / m ]                                                                                           = 11.23 rad / s (c). maximum speed v = A                                   = 7.697 m / s (d). the magnitude of the maximum acceleration of theblock = A ^ 2                                                                                            = 86.44 rad / s ^ 2 where = angular frequency

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