Suppose that a simple pendulum consists of a small 87 g bob at the end of a cord

Question

Suppose that a simple pendulum consists of a small 87 g bob at the end of a cord of negligible mass. If the angle between the cord and the vertical is given by = (0.071 rad) cos[(7.6 rad/s) t + ], what are (a) the pendulum's length and (b) its maximum kinetic energy? Suppose that a simple pendulum consists of a small 87 g bob at the end of a cord of negligible mass. If the angle between the cord and the vertical is given by = (0.071 rad) cos[(7.6 rad/s) t + ], what are (a) the pendulum's length and (b) its maximum kinetic energy? Suppose that a simple pendulum consists of a small 87 g bob at the end of a cord of negligible mass. If the angle between the cord and the vertical is given by = (0.071 rad) cos[(7.6 rad/s) t + ], what are (a) the pendulum's length and (b) its maximum kinetic energy?

Explanation / Answer

here,

mass , m = 0.087 kg

the angular speed , w = 7.6 rad/s

a)

let the length be l

w = sqrt(g/l)

7.6 = sqrt(9.81/l)

l = 0.17 m

b)

amplitude , A = 0.071 rad

the maximum speed , w = A * w

w = 0.012 rad/s

the maximum kinetic energy , KE = 0.5 * I * w^2

KE = 0.5 * 0.087 * 0.012^2 J

KE = 6.3 * 10^-6 J

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