![]() ![]() Where the mass is at, because the graph should agree with what this function's gonna tell us. Whatever position this graph is representing, Value for the position, and that should represent Of the position of this mass as a function of time? So, what would this equation be? Gonna be a function, in other words, you're gonna feed thisįunction anytime you want, and the function's gonna give you, it's gonna spit out a So, we want a function that will be, alright, what is the value Mass has been displaced this way from equilibrium,Īs a function of time. Graph's representing the horizontal position, X, which is how far the Represent this graph here? First of all, what do I even mean by like, the equation for this graph? What I mean is that this However, a lot of times you also need the equation, in other words, you might wanna know whatĮquation would describe this graph right here. Represent any oscillator you want, which is kinda cool. It out horizontally and leaving the amplitude the same, or stretch it both ways to With a larger period, you can imagine stretching This thing vertically, the period would stay the same, but you could stretch out the amplitude. That had a larger amplitude, you can imagine just stretching That's a sine or a cosine, you could represent any motion you want. Time it takes to reset was the time it takes to reset, which would be from peak to peak or from trough to trough or from any point to any analogous point on that cycle, this was the period T. To reset, capital T, is the period, is the And the period, which was the time it took for this entire process And the amplitude of that motion, the maximum displacement from equilibrium on this graph was just represented by the maximum displacementįrom equilibrium, it looked like this. In Section 1.5 we stated that the nature of the oscillation meant that it repeats after every oscillation mathematically \(x(t) = x(t + T)\) the position \(x\) at time \(t\) is equal to the position at time \((t+T)\).Saw that you could represent the motion of a simple harmonic oscillator on a horizontal position graphĪnd it looked kinda cool. In this example, \(F_x\) is considered a restoring force, while \(k\) is the force constant of the spring.Īpplying Newton’s Second Law to this problem, we can obtain the mathematical description of the system: 18.3 Barrier penetration - ‘tunnelling’įigure 1.1: A mass on a spring, stretched distance \(x\) past its equilibrium length \(x_0\)īy Hooke’s law, the spring exerts a force on the block proportional to its displacement \(x\), but in the opposite direction, pushing the block back to its equilbrium position, shown mathematically in Equation (1.1):.18.2 Reflection and transmission of particle waves.18.1 Particle in a square potential well.17.3 Heisenberg’s Uncertainty Principle.17.2 The wavefunction and its interpretation.16.5.1 Lenses side-by-side, zero distance.16.4.2 Ray diagram for a diverging lens.16.4.1 Ray diagram for a converging lens.15.2.3 Considering a convex spherical mirror.15.2.2 Constructing a ray diagram for a spherical mirror. ![]()
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