A 200 g air-track glider is attached to a spring. The glider is pushed in 10 cm and released. A student with a stopwatch finds that 10 oscillations take 12.0 s. What is the spring constant?

Video transcript

Hey, everyone. So this problem is dealing with simple harmonic motion. Let's see what it's asking us. A block with a mass of 0.7 kg is attached to a spring and is oscillating. Calculate the spring constant. If the block completes 16 oscillations in 30 seconds. Our multiple choice answers here are a 7. newtons per meter. B 2.35 newton per meter, C 8.76 newtons per meter or D 3.25 newtons per meter. OK. So this problem is pretty straightforward as long as we can recall our, our period and spring constant equations. So our period T is given by the equation two pi divided by Omega and then our spring constant K is equal to mass multiplied by omega square. Where Omega is that angular frequency? Now, by definition, the period is the oscillations. Is it sorry, is the time per oscillation? Excuse me. So the time her oscillation was given to us in the problem statement. So our period is 30 seconds divided by 16 oscillations or 1.875 seconds. Now we are asked to solve for our spring constant K and So if we use this first equation to uh rewrite our angular frequency in terms of T, we can plug that in. And then we'll have everything we need to solve for K. OK. So that looks like omega equals two pie divided by T and then K equals mass multiplied by two pi divided by T that whole quantity square. We are given masks and the problem of 0.7 kg, two pi divided by T which we solve for 1. seconds. And then that all squared, we plug that into our calculator and we get 7.86 newtons per meter. And that's it. That's the answer to this one. We look at our multiple choice answers that aligns with answer choice A. So that's all we have for this one. We'll see you in the next video.