Question

Suppose that a simple pendulum consists of a small 81 g bob at the end of a cord of negligible mass. If the angle θ between the cord and the vertical is given by θ = (0.068 rad) cos[(9.2 rad/s) t + φ], what are (a) the pendulum's length and (b) its maximum kinetic energy?

Answer 1

Answer:

(a) 0.115 m

(b) 2.08 x 10^-5 J

Explanation:

mass of bob, m = 81 g = 0.081 kg

The equation of oscillation is given by

θ = 0.068 Cos {9.2 t + Ф}

Now by comparison

The angular velocity

ω = 9.2 rad/s

(a) $\omega^{2} =\frac{g}{L}$

where, L be the length of the pendulum

$L =\frac{g}{\omega ^{2}}$

$L =\frac{9.8}{9.2 \times 9.2}$

L = 0.115 m

(b) A = L Sinθ

A = 0.115 x Sin 0.068

A = 7.8 x 10^-3 m

Maximum kinetic energy

K = 0.5 x mω²A²

K = 0.5 x 0.081 x 9.2 x 9.2 x 7.8 x 7.8 x 10^-6

K = 2.08 x 10^-5 J