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) $\frac { d ^ { 2 } \theta } { d t ^ { 2 } } - 2 \theta = 0$

Question

Quizplus · Accepted Answer

The correct linearized differential equation for the angle, $\theta$ , that the swinging pendulum makes with the vertical is $\frac { d ^ { 2 } \theta } { d t ^ { 2 } } + 2 \theta = 0$. This is because the restoring force on the pendulum is proportional to the sine of the angle, and the sine of a small angle is approximately equal to the angle itself.

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

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