### Video Transcript

A type of clock keeps time by
the oscillation of a small object bouncing on a spring. What force constant of a spring
is needed to produce a period of 0.370 seconds for an object of mass 0.0210
kilograms?

Weβll label this force constant
we want to solve for π. And we can start on our
solution by recalling that the period π is equal to two π divided by an
angular speed π and that π for an oscillating spring system is equal to the
square root of the spring, or force constant π, divided by the mass of the
system π.

In the problem statement, weβre
told the values for the period π and the mass π. So, we can combine these two
equations to help us solve for the force constant π. π is equal to two π times one
over π, which is equal to two π times the square root of π over π. When we rearrange this
expression to solve for that force constant π, we find itβs equal to four π
squared times the mass π all divided by the period squared.

Plugging in for π and capital
π, when we enter this expression on our calculator, we find that, to three
significant figures, π is 6.06 newtons per meter. Thatβs the force constant
needed in this oscillating spring to produce this period for this mass.