Question

Simple Harmonic Motion

please explain how do you plug in the formula with the numbers so I can understand it better.

Simple Harmonic Motion - Worksheet Table 1 1 = 1.000 m Amp. = Trial m = 100.0 g 10° T(s) t10 (s) 20° 30° t10 (s) 40° t10 (s) 50° t10 (s) 60° t10 (s) t10 (s) T(s) T(s) T(s) T(s) T(s) 1 2 3 4 5 Average: 80° 70° t10 (s) T(S) t1o (s) T(S) Table 2 Amplitude = 10° m = 100.0 g Length = 1.000 m 0.850 m Trial t10 (s) T(s) t10 (s) T(s) 0.700 m t10 (s) T(s) 0.550 m t10 (s) T(s) 0.400 m t10 (s) T(s) 0.250 m t10 (s) T(s) 1 2 3 4 5 Average: 0.100 m t10 (s) T(s) Period (s) (cal.) % diff. Table 3 Length(n Period (s) (expt) 0.1 0.25 0.4 0.55 0.7 0.85 900.0 g 300.0 g t10 (s) T(S) 500.0 g T(s) 700.0 g tio (s) T(s) 1100.0 g t10 (s) T(S) t10 (s) t10 (s) T(S) Table 4 Amplitude = 10° 1 = 1.000 m Mass = 100.0 g Trial t10 (s) T(s) 1 2 3 4 5 Average:

Answer 1

ANSWER : --

• It can be done simply by applying the following concepts
• first for particular mass determine the time taken to complete the 10 complete oscillation. this will be your t₁₀.
• Now to determine the time period of the oscillation T = Time taken to complete one oscillation= $T = \frac{t_{10}}{10}$
• Now from this we have T, l (given)
• now using the formula $T = 2\pi \sqrt{\frac{l}{g}}$
• $g = 4\pi^{2} \frac{l}{T^{2}}$
• NOW to determine the value of $\frac{l}{T^{2}}$   
• plot the graph between T² vs. l
• determine slope
• now slpoe will be equal to $\frac{T^{2}}{l}$
• $g = 4 \pi^{2}\frac{1}{slope}$ .