A simple pendulum with a length of 2.03 m and a mass of 6.69 kg is given an init

Question

A simple pendulum with a length of 2.03 m and a mass of 6.69 kg is given an initial speed of 1.46 m/s at its equilibrium position.

(a) Assuming it undergoes simple harmonic motion, determine its period.
s

(b) Determine its total energy.
J

(c) Determine its maximum angular displacement. (For large v, and/or small l, the small angle approximation may not be good enough here.)

A simple pendulum with a length of 2.03 m and a mass of 6.69 kg is given an initial speed of 1.46 m/s at its equilibrium position (a) Assuming it undergoes simple harmonic motion, determine its period (b) Determine its total energy (c) Determine its maximum angular displacement. (For large v, and/or small , the small angle approximation may not be good enough here.)

Explanation / Answer

a) for the period

T = 2pi * sqrt(L/g)

T = 2pi * sqrt(2.03/9.8)

T = 2.9 s

the time period is 2.9 s

b)

total energy = 0.50 * m * v^2

total energy = 0.50 * 6.69 * 1.46^2

total energy = 7.13 J

c)

let the maximum angular displacement is theta

m * g * L * (1 - cos(theta)) = total energy

6.69 * 9.8 * 2.03 * (1 - cos(theta)) = 7.13

solving for cos(theta)

theta = 18.8 degree

the maximum angular displacement is 18.8 degree

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