(a) Determine the equation of motion for a pendulum of length 1.5 meters having initial angle 0.2 radians and initial angular de velocity dt 0.3 radians per second. 0(t) = radians (b) What is the period of the pendulum? That is, what is the time for one swing back and forth? Period = seconds
(a) Determine the equation of motion for a pendulum of length 1.5 meters having initial angle 0.2 radians and initial angular de velocity dt 0.3 radians per second. 0(t) = radians (b) What is the period of the pendulum? That is, what is the time for one swing back and forth? Period = seconds
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Transcribed Image Text:Suppose a pendulum of length L meters makes an angle of 0 radians with the vertical, as in the figure. It can be shown that as a
function of time, 0 satisfies the differential equation
L
d20
sin 0 = 0,
L
dt2
where g = 9.8 m/s? is the acceleration due to gravity. For 0 near zero we can use the linear approximation sin(0) - 0 to get a
linear differential equation
d20
0 = 0.
L
dt?
Use the linear differential equation to answer the following questions.
(a) Determine the equation of motion for a pendulum of length 1.5 meters having initial angle 0.2 radians and initial angular
do
= 0.3 radians per second.
dt
velocity
0(t)
radians
(b) What is the period of the pendulum? That is, what is the time for one swing back and forth?
Period =
seconds
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