(a) Determine the equation of motion for a pendulum of length 2.5 meters having initial angle d0 0.3 radians and initial angular velocity 0.5 radians per second. dt 8(t) = (b) What is the period of the pendulum? That is, what is the time for one swing back and forth? Period= radians seconds
(a) Determine the equation of motion for a pendulum of length 2.5 meters having initial angle d0 0.3 radians and initial angular velocity 0.5 radians per second. dt 8(t) = (b) What is the period of the pendulum? That is, what is the time for one swing back and forth? Period= radians seconds
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Transcribed Image Text:Suppose a pendulum of length L meters makes an angle of radians with the vertical, as in
the figure. It can be shown that as a function of time, 0 satisfies the differential equation
d²0
+
d1² L
where g = 9.8 m/s2 is the acceleration due to gravity. For near zero we can use the linear
approximation sin(0) 0 to get a linear differential equation
d²0 8
d1² L
Use the linear differential equation to answer the following questions.
8(t) =
sin 0 = 0,
(a) Determine the equation of motion for a pendulum of length 2.5 meters having initial angle
de
0.3 radians and initial angular velocity = 0.5 radians per second.
dt
Period=
+ -0 =0.
(b) What is the period of the pendulum? That is, what is the time for one swing back and
forth?
seconds
radians.
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