00:01
For this problem, the information that we are given for this is that we have a mass that is equal to four pounds and a spring constant that's called a k that is equal to 25 pounds per feet.
00:28
So considering that the acceleration due to gravity is equal to 32 feet per second square, we need to find the equation of motion.
00:43
So we have in here a mass that is waning four and that is attached to this spring.
00:57
So, first of all, we are going to let, well, letting b.
01:02
M be the mass of the tash and let k be the spreen constant, as we just denoted it in here.
01:08
The newton's second law for this system states that the mass of the object times the second derivative of its position with respect to time, which is the acceleration, is equal to the sprems constant minus the spring constant times the position x.
01:26
Where s is the position or displacement from the equilibrium position.
01:31
We must convert the units of weight given in pounds into units of mass.
01:38
So for example, for the mass m that we are given in pounds, we need to divide that value that we are given by the acceleration due to gravity.
01:52
So we need to divide that by 32.
01:54
So this will give us a value of 1 divided by 8.
02:00
Okay, is lock.
02:03
And so now we can, from this, from the previous expression, we can have that this is, we can divide both sides by the mass, so we will have.
02:22
And we can pass this term to the other side.
02:25
And then this is going to be equal to zero.
02:27
So we are you going to have the second derivative of the displays.
02:31
With respect to time is in this plus the spring's constant divided by the mass.
02:38
This time is the displacement, then this is equal to zero.
02:41
In here, we can recognize that this in here is going to be the angular speed or the angular frequency to the square.
02:49
So we recognize that the angular frequency, the angular frequency is going to be the square root of the sprims constant divided by the mass.
02:59
Okay.
03:02
So we can substitute in here the values that we are given.
03:06
So first of all, this primes constant that we are given for this is 25.
03:11
So we will have 25 divided by 1 divided by 8.
03:19
Okay...