# 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?

We’ll label this force constant we want to solve for 𝑘. And we can start on our solution by recalling that the period 𝑇 is equal to two 𝜋 divided by an angular speed 𝜔 and that 𝜔 for an oscillating spring system is equal to the square root of the spring, or force constant 𝑘, divided by the mass of the system 𝑚.

In the problem statement, we’re told the values for the period 𝑇 and the mass 𝑚. So, we can combine these two equations to help us solve for the force constant 𝑘. 𝑇 is equal to two 𝜋 times one over 𝜔, which is equal to two 𝜋 times the square root of 𝑚 over 𝑘. When we rearrange this expression to solve for that force constant 𝑘, we find it’s equal to four 𝜋 squared times the mass 𝑚 all divided by the period squared.

Plugging in for 𝑚 and capital 𝑇, when we enter this expression on our calculator, we find that, to three significant figures, 𝑘 is 6.06 newtons per meter. That’s the force constant needed in this oscillating spring to produce this period for this mass.