A vertical spring stretches $4\mathrm{.}1$ cm when a $15-$g object is hung from it$.$ The object is replaced with a block of mass $21$ g that oscillates up and down in simple harmonic motion. Calculate the period of motion.

Step $1$

A simple harmonic oscillator moves under the influence of Hooke's law with force

s $=$k

where is the displacement from equilibrium. The spring constant k is given by the following equation.

k $=$

s

$=$

Fsx

When an object of mass m $=15$ g hangs from the spring, the force stretching the spring is

Fs $=$ mg $=$

$15$

$15$

$103$ kg

$9\mathrm{.}80$ m$/$s$2$

$=0\mathrm{.}147$

$0\mathrm{.}147$

N$.$

Step $2$

If this force of magnitude Fs produces an elongation x$,$ the spring constant is

k $=$

Fsx

$=$

N

m

$=$ N$/$m$.$