0:00
Hi there.
00:01
So for this problem, we have a body of mass that is given, and that mass is equal to 500 grams.
00:09
That is the same as 0 .5 kilograms, and is attached to a spring, and the system is driving by an external periodic force of an amplitude that is given.
00:24
That force is equal to 15 neutrons, and a frequency.
00:32
That is also given, that frequency is equal to 0 .7906 hearse.
00:48
Now, the spring stands by a length that is given.
00:52
At that length that we're going to call lower case l is equal to 88 millimeters, which is the same as 88 times 10 to the minus.
01:07
Minus 3 meters under the given load.
01:14
Now, we need to calculate the amplitude of oscillation if the resistance coefficient in the medium is also given, and that we're going to call it b, and that is equal to 5 .05 kilograms per second.
01:34
So we are asking this case about the amplitude, and the amplitude equation is the following.
01:42
Amplitude is just the force divided by the mass, and this divided by the square root of the angular frequency to the square, and this minus the angular frequency of the applied force, minus the angular frequency of the applied force, and that we're going to call p to the square and all of this to the square and this plus a constant gatma that i'm going to define right away this times the again the angular frequency of the applied force and all of that to the square the square root of all of this so we need to find first all of these values so i'm going to start with gatma.
02:49
Gatma is just simply the ratio between b, which is the coefficient, the resistance coefficient of the medium, and this divided by the mass.
03:01
So that will be developed that we are given, 5 .05 kilograms.
03:08
This divided by 0 .5.
03:12
Oh, sorry, this is in kilograms per second, and then the mass is 0 .5 kilograms.
03:19
So the value that we obtained from this is equal to 10 .1 seconds to the minus 1.
03:31
Now i'm going to calculate the angular frequency of the applied force that we call p.
03:39
So that value of p is just simply 2 times pi times the frequency that we are given.
03:46
So that will be 2 times pi times the frequency that in this case is 0 .796.
03:56
So hers, so from this we obtain a value of.
04:08
So we can approximate a value to 5.
04:11
5 radiance per second.
04:15
Now we are going to calculate the force constant of the spring.
04:24
That force constant is just simply.
04:26
That the force that we are given, divided by the length.
04:30
So that will be the mass times acceleration due to gravity, which is the weight...