course Phy 231
For a certain pendulum, periods of T = .29, .4084402, .4990342 and .5752532 seconds are observed for respective lengths L = 4, 8, 12 and 16 units. •Determine whether the transformation T -> T2 or T -> T3 linearizes the function better.
Answer: By inspection of a graph the line is straighter for the transformation T ->T^2, therefore it linearizes the function better.
• Determine the equation of the resulting straight line, and solve the equation for T.
Answer: m = rise/run = (16 – 4) / (.5752532 - .29) = 42, y = mx +b, 4 = 42(.29) + b, 4 = 12.18 + b, b=-8.18, replacing x with T and y with L, L=42T – 8.18, 42T = L + 8.18, T = L/42 + .19.
• Use your equation to determine the period of a pendulum whose length is 14.50471 units.
Answer: T = (14.50471)/(42) + .19 = .5353502 seconds.
• Use your equation to determine the length of a pendulum whose period is 1.220222 seconds.
Answer: L = 42T – 8.18 = 42(1.220222) – 8.18 = 43.06932 units.
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