A 0.500-kg glider, attached to the end of an ideal spring with fo...

Question

A 0.500-kg glider, attached to the end of an ideal spring with force constant k = 450 N/m, undergoes SHM with an amplitude of 0.040 m. Compute (b) the speed of the glider when it is at x = -0.015 m.

Accepted Answer

Welcome back everybody. We are taking a look at a harmonic oscillator. That kind of looks something like this. We have a string or sorry, a spring attached from some surface attached to an object. And so it's moving up and down right at some point, there is an equilibrium point and we are told a couple of different things about this entire system. First we are told that the mass of the hanging object is 0.25 kg. We're also told that the spring constant Is 100 newtons per meter. And then we are also told that the maximum displacement, the maximum position away from the equilibrium point that this object reaches is five cm or . m. And we are tasked with finding what the speed is of this object when it is at a position of negative two cm below the equilibrium or negative 0.02 for this, we are going to use the principle of the conservation of mechanical energy. That says that the total mechanical energy is equal to the kinetic energy plus the potential energy. This translates to this equation right here, one half M V squared plus one half Pay x squared equal to one half a squared. So, using a little bit about solving for V. Here, we're gonna have that V is equal to plus or minus the square root of the spring constant over the mass of our object. Times the square root of our maximum displacement squared minus the position. We're looking at squared. Now, since we are look at speed here, speed is just the magnitude of velocity. The speed is going to be a positive number. Let's go ahead and plug in all these values. Since we know that we have the square root of 100 are spring constant over our mass of 0.25 kg times the square root of our maximum displacement. 0.5 squared. Let me extend this radical a little bit minus negative 0.2 squared the position at which we're trying to calculate the velocity when you plug all this into your calculator, you get that. Our final answer is 0.91 m per second corresponding to answer choice. C Thank you all so much for watching. Hope this video helped. We will see you all in the next one.

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