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, satisfies the differential equation d20 + sin = 0, dt2 L where g = 9.81 m/s² is the acceleration due to gravity. For near zero (small) we can use the linear approximation sin(e) to get a linear differential equation d20 dt2 -+10=0. Answer the following questions. The pendulum of length 2 meters have initial angle 0.1 radians and initial angular de velocity =0.5 radians per second. dt (a) What is the amplitude of the pendulum? 0m radians (b)Determine the equation of motion for the pendulum
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, satisfies the differential equation d20 + sin = 0, dt2 L where g = 9.81 m/s² is the acceleration due to gravity. For near zero (small) we can use the linear approximation sin(e) to get a linear differential equation d20 dt2 -+10=0. Answer the following questions. The pendulum of length 2 meters have initial angle 0.1 radians and initial angular de velocity =0.5 radians per second. dt (a) What is the amplitude of the pendulum? 0m radians (b)Determine the equation of motion for the pendulum
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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, satisfies the differential equation
d20 9
+ sin = 0,
dt2 L
where g = 9.81 m/s² is the acceleration due to gravity. For near zero (small) we can use the linear
approximation sin(6) ≈ to get a linear differential equation
d20
+
dt2
10=0.
Answer the following questions. The pendulum of length 2 meters have initial angle 0.1 radians and initial angular
do
velocity = 0.5 radians per second.
dt
(a) What is the amplitude of the pendulum?
Om
radians
(b)Determine the equation of motion for the pendulum
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
Ꮎ
L
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