A Pendulum of Length $l$ Hangs from the Ceiling $g$ Represent the Gravitational Acceleration

question 14

Multiple Choice

A pendulum of length $l$ hangs from the ceiling. Let $g$ represent the gravitational acceleration. The correct linearized differential equation for the angle, $\theta$ , that the swinging pendulum makes with the vertical is

• A) \(\frac { d \theta } { d t } + g \theta / l = 0\)
• B) \(\frac { d ^ { 2 } \theta } { d t ^ { 2 } } + g \theta / l = 0\)
• C) \(\frac { d \theta } { d t } + l \theta / g = 0\)
• D) \(\frac { d ^ { 2 } \theta } { d t ^ { 2 } } + l \theta / g = 0\)
• E) \(\frac { d ^ { 2 } \theta } { d t ^ { 2 } } - g \theta / l = 0\)

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Definitions:

Dependent Variable

In an experiment or study, it's the variable being tested and measured, which is expected to be influenced by another variable (the independent variable).

Dependent Variable

A variable in a scientific experiment that changes in response to the manipulation of the independent variable.

Independent Variable

In research, the variable that is manipulated to observe its effect on a dependent variable.