1. Draw by hand a graph of displacement vs. time for an...

1. Draw by hand a graph of displacement vs. time for an oscillating spring with spring constant, k = 0.64 N/m, and hanging mass, m = 0.25 kg. 2. From your graph in #1, draw graphs for the velocity of the moving end of the spring, v, as a function of time and also the acceleration of the moving end of the spring, a, as a function of time (these don't have to be drawn numerically precisely, but keep your t-axis scale the same for all three graphs). 3. Discuss the implications of the relation between position, velocity, and acceleration in a simple harmonic oscillation system.

Transcript

00:03 In this question, you have three sub questions, which i copied down here.

00:06 The first question i ask you to draw behind the graph of the displacement as a function of time for oscillating spring with spring constant key and a honey mice.

00:18 So let's have a look.

00:20 Suppose the spring, this basic is harmonic calculator, right? suppose you have something, a roof, a ceiling, okay, is singing and you have a harmonica you have some spring and some mass um okay a honey down and this spring constant k and then i want to do a graph which choose the displacement versus time right so question one i want to do a graph i do a graph like this and this is time t and this is displacement.

01:03 Let me choose the displacement to be direction.

01:07 Let me choose the direction to be something like this.

01:10 I call it x.

01:12 So this is x.

01:13 So x is function of a t.

01:15 Well, depending on, so suppose the equilibrium position that would take it to be x equals zero, okay? x equals zero is the equilibrium position.

01:25 And if i start, if i sort of think that in a, the harmonic strategy is actually oscillating.

01:33 Therefore, i would like to release it when, i would say, i would like to assume that for simplicity, when t was zero and x equals the maximum, okay, which is at dinner by x.

01:46 So suppose the mass will be somewhere here.

01:50 First, i compress the spring and so the mass is somewhere here.

01:55 Let's say this is x, m -a -x, right? and then i release the spring, then it's going to start to oscillate.

02:04 So at t equals zero, the disbursement, the big, the fixed, right? so i'm going to draw that disbursement, which starts fixed, and then it goes down and it's going to oscillate.

02:21 And it's going like this, right? so it's cosine harmonic wave, i assume.

02:27 And then how about, how about, for example, the second question you asked to look at, for the velocity as function of time and acceleration as well.

02:42 So i'm going to join this way.

02:48 Okay, so let me remove this label.

02:54 And i will call this one, i will just elaborate, you know, this guy is x.

03:01 The disbursement is function of velocity, right? it's a cosine wave.

03:06 Now let's ask ourselves what the velocity could be, right? i use a blue line for the velocity.

03:14 I put it here.

03:15 So velocity, you know, when at the beginning, when the displacement is fixed of use the velocity is zero and then therefore if velocity is zero and the next moment that is going downward, right? because push is going downward.

03:32 And the, and the, i think, velocity i'm showing actually here.

03:44 So actually, i made a little bit of mistake.

03:46 I would like to, i should have put the, sorry, this thing, the axis should not be going like this.

03:58 It should actually go upward.

04:00 I wanted to go upward rather than...

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