Find the period of small oscillation of a simple pendulum of length ' ℓ ' if its point of suspension O moves relative to the earth with a constant acceleration a , given ℓ = 10 2 cm and ∣

Question

Find the period of small oscillation of a simple pendulum of length ' $ℓ$ ' if its point of suspension O moves relative to the earth with a constant acceleration $\overline{a}$ , given $ℓ = 102 cm$ and $∣ \overline{a} ∣ = 5 g$ and the angle between the vectors $\overline{g}$ and $\overline{a}$ is $β = 12 7^{\circ}$ . The period of oscillation of the pendulum is approximately :

TestHub · Accepted Answer

Effective gravity: g e ff ​ = g 2 + a 2 − 2 g a cos 12 7 ∘ ​ with a = 5g and cos 12 7 ∘ = − 0.6 . g e ff ​ = g 1 + 25 + 6 ​ = 4 2 ​ g T = 2 π g e ff ​ ℓ ​ ​ = 2 π 40 2 ​ 0.1 2 ​ ​ ​ = 2 π × 0.05 = 0.314 s Answer: C

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