Suppose that a simple pendulum consists of a small 80 g bob at the end of a cord

Question

Suppose that a simple pendulum consists of a small 80 g bob at the end of a cord of negligible mass. The angle between the cord and the vertical is given by the following formula. 0(t) = (0.080 rad) cos[(4.36 rad/s) t + (a) Calculate the pendulum's length 515 (b) Calculate its maximum kinetic energy. 002 (c) At t=0, the pendulum is started from the vertical with a push in the direction where is denoted as positive. Please give the smallest positive phase angles that could be used to describe this system. (Express as a multiple of P4 | 7.414

Explanation / Answer

Here ,

mass of bob , m = 0.080 Kg

a) as anglular speed , w = 4.36 rad/s

let the length of pendulum is L

as w = sqrt(g/L)

4.36 = sqrt(9.8/L)

L = 0.515 m

the length of the pendulum is 0.515 m

b) for the maximum kientic energy of pendulum

KE = 0.5 * I * w^2

KE = 0.5 * m * L^2 * (0.080 * 4.36^2)

KE = 0.5 * 0.080 * 0.515^2 * (0.080 * 4.36)^2

KE = 1.29 *10^-3 J

c)

as the pendulum is moving to the positive , with the pendulum at the zero

phi = 0 * pi radian

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