A pendulum consists of a mass m attached to the end of a rod of length L. The pendulum is displaced from its equilibrium position by an angle of 0 radians. Assume no air resistance or friction in the motion of the pendulum. See figure below. 8 L Fill in the blank to write a differential equation to model the motion of the pendulum for any angle 0. d²0 dt² = -gL sin(0) ✓ Is this differential equation linear or nonlinear? ⚫ nonlinear linear πT πT Now, assume the angle 0 is small (that is, < 0 ≤ Ꮎ 12 radians or -15° ≤ 0 ≤ 15º), and make an appropriate substitution to simplify the equation above. 12 d²0 = -gL sin(0) dt2 ✓
A pendulum consists of a mass m attached to the end of a rod of length L. The pendulum is displaced from its equilibrium position by an angle of 0 radians. Assume no air resistance or friction in the motion of the pendulum. See figure below. 8 L Fill in the blank to write a differential equation to model the motion of the pendulum for any angle 0. d²0 dt² = -gL sin(0) ✓ Is this differential equation linear or nonlinear? ⚫ nonlinear linear πT πT Now, assume the angle 0 is small (that is, < 0 ≤ Ꮎ 12 radians or -15° ≤ 0 ≤ 15º), and make an appropriate substitution to simplify the equation above. 12 d²0 = -gL sin(0) dt2 ✓
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:A pendulum consists of a mass m attached to the end of a
rod of length L. The pendulum is displaced from its
equilibrium position by an angle of 0 radians. Assume no air
resistance or friction in the motion of the pendulum. See
figure below.
8
L
Fill in the blank to write a differential equation to model
the motion of the pendulum for any angle 0.
d²0
dt²
=
-gL sin(0)
✓
Is this differential equation linear or nonlinear?
⚫ nonlinear
linear
πT
πT
Now, assume the angle 0 is small (that is,
< 0 ≤
Ꮎ
12
radians or -15° ≤ 0 ≤ 15º), and make an appropriate
substitution to simplify the equation above.
12
d²0
=
-gL sin(0)
dt2
✓
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