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Simpson’s Rule:
4.12.4cose5.2)(M 4.1
0
?d)(M
-1.4
4.2i
427.42.44.1 220
316.0427.4
4.1
49.4316.0419.1T0
s
419.1427.422
T0
0
49.4
0
?d)(M
3742.012
049.4
12n
Example: Calculate the integral of the given function.
From a vibration measurement on a machine, the damping ratio and undamped vibration frequency are calculated as 0.36 and 24 Hz, respectively. Vibration magnitude is 1.2 and phase angle is -42o. Write the MATLAB code to plot the graph of the vibration signal.
Example:The temperature (T) of a medical cement increases continuously as the solidification time (t) increases. The change in the cement temperature was measured at specific instants and the measured temperature values are given in the table. Find the cement temperature at t=36 (sec).
68*)1555)(555(
)15t)(5t(43*
)5515)(515()55t)(5t(
30*)555)(155()55t)(15t(
)t(T
C51.6168*)1555)(555()1536)(536(
43*)5515)(515()5536)(536(
30*)555)(155(
)5536)(1536()t(T o
Lagrange Interpolation:
Example:The buckling tests were performed in order to find the critical buckling loads of a clamped-pinned steel beams having different thicknesses. The critical buckling loads obtained from the experiments are given in the table. Find the critical buckling load Pcr (N) of a steel beam with 0.8 mm thickness.