In a physics lab, you attach a 0.200-kg air-track glider to the end of an ideal spring of negligible mass and start it oscillating. The elapsed time from when the glider first moves through the equilibrium point to the second time it moves through that point is 2.60 s. Find the spring's force constant.

Video transcript

Hey everyone in this problem we're told that there are various methods of determining the spring force constant of a spring. One method involves measuring the mass and oscillation times. For the mass. In one setup we use a mass of 0.82 kg and measure the time it takes the mass to move from a point negative a to the next instance. It comes back to the same point to be 3.2 seconds. Okay. And we're asked what is the force constant for the spring? Alright, so when we're talking about The time it takes to move from point negative a back to the next instance we come back to that exact same point. Okay, that's the definition of a period. Okay so the period T is going to be equal to 3.2 seconds in this case. Okay. Alright so we have the period T. Okay, we also know the mass 0.82 kg. And we're trying to find. Kay well let's recall that we can relate the angular frequency omega to two pi over the period T. Okay, we know T. And omega. The angular frequency is also equal to the square root of K over em So we're trying to find this force constant K. We know the period T. And we know the mass. Okay, so we can use this formula, substitute the values we know and solve for K. Alright so we get two pi divided by this period 3.2 seconds is equal to the square root of K. Divided by the mass 0.82 kg. Alright if we square both sides, we have two pi divided by 3.2 seconds. All squared is equal to K divided by the mass. 0.82 kg. Okay. And multiplying by that mass, we get that K is equal to two pi over 3. seconds. All squared times 0. kilograms. Okay? And if we work this out, We are going to get that. This force constant K is approximately 3. newtons per meter. Okay. Alright, so this is our spring force constant 3.16 newtons per meter. And that is going to be answer. E. That's it for this one. Thanks everyone for watching. See you in the next video.