Mathematics, 05.05.2021 07:20, vanessasantos2004vs

(1 point) Suppose a pendulum of length L meters makes an angle of θ radians with the vertical, as in the figure. It can be shown that as a function of time, θ satisfies the differential equation
d2θdt2+gLsinθ=0,
where g=9.8 m/s2 is the acceleration due to gravity. For θ near zero we can use the linear approximation sin(θ)≈θ to get a linear differential equation
d2θdt2+gLθ=0.
Use the linear differential equation to answer the following questions.

(a) Determine the equation of motion for a pendulum of length 2 meters having initial angle 0.4 radians and initial angular velocity dθdt=0.1 radians per second.

θ(t)=
0.4cos(2.21t)+0.09sin(2.21t)
radians

(b) What is the period of the pendulum? That is, what is the time for one swing back and forth?

Period =
2sqrt10/sqrt49pi
seconds

Answers: 2

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(1 point) Suppose a pendulum of length L meters makes an angle of θ radians with the vertical, as...