Question

A mass of 8kg is suspended from a spring with a spring constant of 16N/m and then released, creating periodic motion. At what distance below the natural length of the spring will the mass finally come to rest?
a. 4.9m
b. 9.8m
c. 19.6m
d. 7.2m

Answer 1

The spring will come to rest 4.9 m below the natural length

Explanation:

The mass-spring system will come to rest when the restoring force on the spring (pulling upward) balances the weight of the mass (pulling downward). Mathematically, this can be written as

$F_x = W\\kx = mg$

where

k is the spring constant

x is the elongation of the spring

m is the mass

g is the acceleration of gravity

In this problem, we have:

$m = 8 kg$ is the mass

$g=9.8 m/s^2$ is the acceleration of gravity

$k=16 N/m$ is the spring constant

Solving the equation for x,

$x=\frac{(8)(9.8)}{16}=4.9 m$

Therefore, the spring will come to rest 4.9 m below the natural length.

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