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A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.500 s for a 0.0150 -kg mass?

$K=2.36 \mathrm{N} / \mathrm{m}$

Physics 101 Mechanics

Physics 103

Chapter 16

Oscillatory Motion and Waves

Periodic Motion

Wave Optics

Rutgers, The State University of New Jersey

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in this problem. We're going to talk about the elastic force, particularly the one coming from spring. So let's say that we have a block of mass and attached to the end of the stream. And let's say you fool the block by a distance X So the force is equal to the spring Constant actually minus the spring constant. Okay, Times X where access Positive. If we're pulling Thea object and negative If we're pushing Also, let's say you pull the object by this distance acts uh and you let the object just, uh, vibrate. So it was start at a certain position. It will be compressed, completely black, compressed. And then after that, it will come back to the original position and so on. Basically, it will start vibrating and balancing with a new angular frequency omega that is equal to the square root off K over em. Now, remember that the frequency, the angular frequency is two pi divided by the period t so we can calculate the period t as two pi times am over. Kate. And this is the period off oscillation off the spring. And in our problem, our goal is to calculate what must be the force. The first constant K of the spring given that M the mass is equal to 0.0 15 kg and that we want the period to be, which is your point? Five seconds s. So basically, I'm gonna isolate K here. Eso I'm gonna square both sides. We have that k is equal to four pi square am divided by t squared. So K is four pi squared times 0.0 15 kg divided by 0.5 seconds squared. This is equal to two point 27 Newton screw meter which answers air exercise.

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