Movement of damped oscillations during earthquakes

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Reference no: EM131076598

1) Structural engineers may have to study the movement of damped oscillations during earthquakes. One equation that gives the horizontal displacement of an object as a function of time is:

X = Xoe
-βt[cos(wt) + (β/ω)sin(ωt)]

The parameters β and ω depend on the mass of the oscillating object and the dynamic characteristics of the system. Other variables are defined as follows:
Xo = 8 inches,
β = 0.1 sec-1

ω = 0.1 sec-1
Using Excel, start a new worksheet titled Oscillation.
A) Prepare a table of t versus X over the interval of 0 ≤ t ≤ 30 seconds using 1 second intervals.

B) Using absolute references, solve the equation above for the range in A.

C) At approximately what time does the displacement (x-value) approximately equal zero? (or in other words, estimate the value of t corresponding to x = 0). Highlight using a bright yellow color, the two times (t) that bracket a displacement of x =0.

Your worksheet should look like the following and the boxed region should be filled with the equation.
Remember to highlight the time where the displacement changes from positive to negative using a bright yellow
background color.

2) Create another worksheet title "Trig functions"

a) Create a series in column A, titled "Angle (Degrees).
b) Fill a series in column A under degrees, going from 0 to 360 in increments of 10
c) In nearby columns, calculate the sin, cos and tan of each angle
d) Format the answer for sin, cos and tan to a "number" with 3 fixed decimal places
e) Using you calculator, compute the tan (90°) and the tan (π/2). Put the computed values in the spreadsheet to the side of the columns.
f) Are the values from the calculator and the value from the spreadsheet at degrees = 90 the same? Should they be the same? Any guesses as to why they are different?

Your spreadsheet should look something like this with the COS, SIN and TAN columns filled in.

3) Start a new sheet called "area"
Calculate the area of a circle with a diameter = 100 ft.

a) using the function pi() inside excel
b) using a value of 3.1416 for PI.
c) Is there a difference between the values? If yes, explain why there would be a difference.

Boxes should be filled in with your answers with an explanation below them

Reference no: EM131076598

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