FIGURE EX15.7 is the position-versus-time graph of a particle in simple harmonic motion. a. What is the phase constant?

Video transcript

Welcome back, everyone. We are given this position time graph here. And we are tasked with finding what is the phase constant of motion. What we can use is that for simple harmonic motion, we can use this position formula that X at time T is equal to the amplitude times the cosine of omega T plus our phase constant here. Now at T equals zero, we can see that our displacement X is also zero. So let's plug that in, we have zero is equal to our amplitude times our cosine of zero plus our phase constant. Now dividing both sides by our amplitude, the amplitude just dis disappears. And then we will take the inverse cosine of both sides. And we get that our phase constant is equal to the inverse cosine of zero, which can either be positive or negative pi over two. But which one is it? Well, here are the kind of some rules of the, the phase constant here. If we have that after time T we have that we are approaching a negative amplitude. This leads us to having a positive face constant. But if at after time T we are approaching a positive amplitude. That means we will have a negative phase constant. As you can see, we are approaching a positive amplitude. Therefore, our phase constant must be negative making our phase constant for this position time graph negative pi over two which corresponds to our final answer. Choice of C Thank you all so much for watching. I hope this video helped. We will see you all in the next one.