# Video: Calculating Spring Constant for a Spring-Based Clock

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 s for an object of mass 0.0210 kg?

01:25

### 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?

Weβll 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, weβre 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 itβs 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. Thatβs the force constant needed in this oscillating spring to produce this period for this mass.