Pendulum terminology in engineering mechanics A rigid body suspended vertically from a fixed point and oscillating with a small amplitude under gravity is termed what type of pendulum?

Introduction / Context:
In engineering mechanics and vibrations, the term used for a rigid body swinging about a fixed horizontal axis under gravity is important for selecting correct formulas for time period and center of oscillation. Many learners confuse “simple pendulum” with “compound” (also called “physical”) pendulum.

Given Data / Assumptions:

• The body is rigid (not a point mass and not a massless string).
• It is suspended to swing about a fixed horizontal axis under gravity.
• Amplitude is small so the small-angle approximation applies.

Concept / Approach:

A simple pendulum is an ideal model: a point mass suspended by a weightless inextensible string. A compound pendulum (also called a physical pendulum) is any rigid body oscillating about a fixed horizontal axis under gravity. Its dynamics depend on the body’s mass moment of inertia about the suspension axis and the distance of its center of gravity from that axis.

Step-by-Step Solution:

Verification / Alternative check:

The time period for a compound pendulum is T = 2 * pi * sqrt(I_o / (m * g * h)), where I_o is the mass moment of inertia about the suspension axis and h is the distance from the suspension axis to the center of gravity. This formula explicitly requires a rigid body, confirming the classification.

Why Other Options Are Wrong:

Simple pendulum assumes a point mass and string; second's pendulum is a special simple pendulum with T = 2 s; “none” is incorrect because the standard term exists.

Common Pitfalls:

Interchanging “simple” and “compound”; overlooking that “physical pendulum” is synonymous with “compound pendulum”.

Final Answer:

Compound pendulum