Question

A block of mass m = 0.672 kg is fastened to an unstrained horizontal spring whose spring constant is k = 97.0 N/m. The block is given a displacement of +0.162 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.

Answer 1

Given,

The mass of a block, m = 0.672 kg

The spring constant, k = 97 N/m

The displacement, x = 0.162 m

a)

The force, F = - k x

= - 97 * 0.162

= 15.714 N

The negative sign indicates that the force is restoring.

b)

We know,

The spring constant, k = m * ²

= √ (k / m)

= √ (97 / 0.672)

= 12.014 rad/s

c)

The maximum velocity, V _max = A *

= 0.162 * 12.014

= 1.946 m/s

d)

The maximum acceleration, a_max = ² *A

= (12.014)² * 0.162

= 23.382 m/s²