In concept simulation 10.3 you can explore the concepts that are important in this problem. a block of mass m = 0.629 kg is fastened to an unstrained horizontal spring whose spring constant is k = 99.9 n/m. the block is given a displacement of +0.120 m, where the + sign indicates that the displacement is along the +x axis, and then released from rest. (a) what is the force (with sign) that the spring exerts on the block just before the block is released? (b) find the angular frequency of the resulting oscillatory motion. (c) what is the maximum speed of the block? (d) determine the magnitude of the maximum acceleration of the block.

Following are the solution to the given points:

For part A)

The force exerted by the spring can be calculated using Hooke's law as follows:

As a consequence, the season's force is as follows:

(The -ve symbol denotes that the force exerted by the spring is in the opposite direction).

Calculating the three significant figures:  

 For part B)

The angular frequency of oscillatory motion is given by:

 Calculating the three significant figures:

 For part C)

maximum speed in SHM movement is provided by:

 So,

   For part D)

The maximum acceleration of the block is given by:

 Calculating the three significant figures:

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Explanation:

a) F = -kx = -99.9 * 0.12 = -11.988N

b)

Using for x,v,a :

gives the angular frequency:

ω = 12.6 1/s

c) v is max, when :

d) a is max, when :

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