Homework #3
P=ENED 1090:
Engineering Models I
Homework Assignment #3
Due:
September 23, 2016 at 5:00pm
Problem 1: Simple Harmonic Motion
Sinusoids are used to model simple harmonic motion as illustrated in the figure below that shows
a mass attached to a spring.
If we assume no loss of energy, the displacement of the mass looks
like a cosine wave.
In this lab, we will assume the oscillations are undamped.
Assuming simple harmonic motion, the displacement of the mass is given by:
A
=
Initial Displacement of Mass (m) (how much spring is compressed initially)
K
=
Spring Constant (N/m)
M
=
Mass of suspended mass and spring (kg)
t
=
Time (s)
The velocity of the mass is the derivative of displacement with respect to time:
The kinetic energy and the potential energy (both in units of Joules) can be calculated as follows:
(m/s)
1
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Homework #3
Write a script file that does the following:
1.
Prompts the user using input statements for initial displacement, A, spring constant, K,
and the mass, M.
2.
Calculates the frequency of oscillation:
3.
Calculates the period, T.
4.
Uses fprintf statements to output the frequency of oscillation and the period with four
places behind the decimal point for each.
Include units in your output statements.
5.
Creates a vector of values for time, t, that starts at 0 and ends at 3T.
6.
Calculates position, p, velocity, v, kinetic energy, KE, and potential energy, PE, for the
time vector created in step 5.
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 Fall '15
 Dr.Kastner
 Ode

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