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

Question

Quizplus · Accepted Answer

The correct linearized differential equation for a pendulum is $\frac { d ^ { 2 } \theta } { d t ^ { 2 } } + \frac{g}{l} \theta = 0$, which describes the angular acceleration ($\frac { d ^ { 2 } \theta } { d t ^ { 2 } }$) in terms of the gravitational acceleration ($g$) and the length of the pendulum ($l$). This equation assumes small angles for $\theta$, where $\sin(\theta) \approx \theta$ in radians.

A Pendulum of Length lll Hangs from the Ceiling ggg Represent the Gravitational Acceleration

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