00:01
So we have a frictionless spring, the mass attached is going to be 10 kilograms.
00:09
We're told that this can stretch to a maximum of 1 .8 meters if the force applied, so if the force applied is equal to 50 newtons.
00:27
And so what this looks like is a spring system, of course with a spring constant attached to the mass m.
00:35
We'll call this the equilibrium position and we'll call the stretching the amplitude, so we know it goes that way in the opposite direction as well.
00:47
That'll be the equilibrium position and this will be x.
00:52
The distance between them is 1 .8 and the force applied will be in this direction, so that means that the spring force will want to restore it back to the equilibrium position.
01:04
It'll be in the opposite direction.
01:06
This means that we can find a equation, or rather a value for the parameters we need.
01:13
Let's go ahead and write what else we have.
01:14
We have the initial velocity, a little push of 1 .5 meters per second and we are also told that well, the friction is zero, so i'm going to put mu equals zero.
01:32
Now we want to figure out the position.
01:35
It's a t -second, so when it says position after t -seconds, that suggests that we need the sinusoidal form of position.
01:46
It's a t which will be equal to an amplitude times cosine of an angular frequency, omega times t, plus a phase shift, plus a vertical shift.
01:58
So we need this equation.
02:02
Now we're going to assume, since we have a positive position at t equals zero when it's stretched out to the furthest, we're going to say that x of t will be equal to, so far we can say, a cosine of omega t.
02:19
Now, no phase angle as well, so we're just going to leave zero here and no vertical shift as far as we know, so we're going to have this as zero.
02:27
And then we just get a cosine of omega t.
02:32
But we know a, and it needs to be 1 .8, and we can figure out omega...