ea 3 project

7/29/2019 EA 3 Project

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Problem 1

The goal of this problem is to find the velocity to shoot a pellet into a receiving tube, given a

definite height and distance to shoot. For the first part of the problem, no air drag is taken into

account. The second part of the problem takes into account air drag.

For this problem, the mass of the pellet is 0.1 kg, the drag is coefficient is from 0.01 to 0.03 kg/m,

the height of the tube is 10 meters, and the length the pellet travels is 10 meters. The pellet needs

to enter the receiving tube with essentially zero vertical component.

For the zero drag case,

The velocity was found to be 15.65 m/s, and the angle was at 63.44 degrees to the horizontal.


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With air drag, the code was done to loop through specific terms for theta and velocity in order to

find the correct velocity it took given a specific air drag. Though the code was not completely

correct (still working on the code, it is incomplete) since theta seemed to be incorrect, the

velocity seemed to hover around 35 meters per second and the angle was slightly below the case

with air drag, so it was around 55 to 60 degrees.


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Problem 2

The goal of this problem is to obtain the state equations of a 12 mass 12 spring system,

connected all in series.

In order to get a 12 mass 12 spring matrix, I first looked at 1 spring 1 mass, 2 spring 2 mass, and 3 spring

3 mass systems. I was then able to find a pattern to generalize for the 12 spring 12 mass case.

I noticed that all the springs had a -1 and 1 term, and each -1 term came two spots under the 1 for the

previous spring.

For the masses, the non zero values occurred one spot before and after the diagonalm and the spring

constants were one below and above the mass, with the first term being negative. For instance, if this is

the fourth mass, then the first term in the sequence isk3/m4, and the term two columns away is k5/m4.

From this, the 24 spring 24 mass case was generalized.


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For this problem, a MATLAB code was written in order to solve the matrix, and the code was run for all

masses 1 kg and all springs with spring constant of 10 N/m. The force source had a pulse of 100 N for 0.1

seconds. The resulting motion of each spring was found and are plotted in 12 separate graphs below:


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As evident from the graphs, the springs all had their stretches increase, though 12 had its stretch increase

the fastest since it was right next to the force. Spring 1 stretched very near the 0.1 second mark. Spring


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12s stretch increase very steadily, while most of most of the other springs had no stretch to start off and

then a sudden increase.

For the last part of the question, the tenth mass was taken to be 1000 kg. In this case, the mass is

like a wall since it is so huge, so it oscillates for the two masses and basically bounces back.For instance, when the mass is normal, it pulses down to the end and bounces back, but when the

mass is big, it pulses to that mass and bounces back. In this case, the other masses are

propagating off the tenth mass, and the pulse gets stronger and stronger.

Problem 3

A 100 segment of a cable consists of 20 inductors and 20 capacitors lumped over each 5 meter

segment in this cable. The capacitance of the cable is 100 picofarad per meter, and the

inductance is 0.25 microhenry per meter. A 1V input pulse of 0.1x10-6

seconds is enforced.

For this problem, the pulse propagation through the cable is monitored for a total of 3

microseconds for a time step of 0.01 micro seconds. The goal of this problem is to figure out the

speed in which the input voltage pulse propagates in this cable by using numerical approximation.

The program tline64.m was adjusted to work for the values given above and also to work for 20

inductors and 20 capacitors. In order to approximate the speed with which the input voltage pulsepropagates, I looked at the time it took for the wave to travel from the start to end, one period,

and divided this time by 100 meters to get the speed. Using my approximation, I got a total speed

of about 1.88 x 10^7 m/s.

Problem 4

An RLC tuner circuit was discussed in class, and an example code tone_control.m was shown.

For this problem, the code was adjusted for two cases1) so that the output is more base

(frequencies about 500 Hz are emphasized) and 2) the output is mid-range (about 1500 Hz). Thevalues for L and C in the circuit had to be changed, and the time and frequency of the input and

output were plotted.

For the base 500 Hz case, the goal was to look for spikes on the V output graph at the 500 Hz

mark. The following graphs were obtained:


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For these graphs, the L value was 0.5, and

the C value was 0.0001. These numbers

corresponded to the points where the spikes

were closest to the correct frequency.

The same procedure was done for the 1500 Hz case:

In this case, the L value was approximated to be0.0005, and the C value was 0.0001.

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