The mathematical pendulums, the length ratio of which is L1 / L2 = 4, were deflected by the same
| August 13, 2021 | education
The mathematical pendulums, the length ratio of which is L1 / L2 = 4, were deflected by the same angle and released. What is the ratio of their maximum speeds v1 and v2?
These problems: k (the ratio of the lengths of the indicated mathematical pendulums) = Lm1 / Lm2 = 4 p.
We find the ratio of the maximum speeds of the indicated pendulums by the formula: n = V1 / V2 = A * ω1 / (A * ω2) = (2Π / Tm1) / (2Π / Tm2) = Tm2 / Tm1 = 2Π * √ (Lm2 / g) / (2Π * √ (Lm1 / g)) = √ (Lm2 / g) / (Lm1 / g) = √ (Lm2 / Lm1) = √ (Lm2 / Lm1) = √4 = 2 p.
Answer: The ratio of the maximum speeds of these pendulums is 2.
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