A Pendulum of Length 16 Feet Hangs from the Ceiling $g = 32$

question 27

Multiple Choice

A pendulum of length 16 feet hangs from the ceiling. Let $g = 32$ represent the gravitational acceleration. The correct linearized differential equation for the angle, $\theta$ , that the swinging pendulum makes with the vertical is

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

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Definitions:

Lecithin

A fatty substance found in plant and animal tissues, acting as an emulsifier in food products.

Long-chain Alcohols

Alcohols containing a long chain of carbon atoms, typically more than twelve, used in detergents, emulsifiers, and solvents.

Fatty Acids

Long-chain hydrocarbon molecules with a carboxylic acid group, important as sources of energy and as components of cell membranes.

Sodium Palmitate

A sodium salt of palmitic acid, used in soap making and as a surfactant in cosmetics.