The frequency of a body executing simple harmonic motion when left undisturbed is known as__________ frequency.

Analyze the question: It asks for the name given to the frequency at which a body oscillates in SHM when it is left undisturbed, meaning no external force is acting on it after the initial displacement.

Concept:

• Natural frequency: the frequency at which a system vibrates by itself when disturbed once and then left alone. It depends only on the properties of the system, such as mass and spring constant, or the length of a pendulum.
• Free vibration: the type of oscillation that happens when there is no external driving force.
• Forced frequency: the frequency of an external periodic force driving the system.
• Damped: the oscillation loses energy because of resistance, so the amplitude decreases.
• Sinusoidal: describes the shape of the displacement-time graph, not a type of frequency.

Working through the options:

• A. Damped: this describes loss of amplitude, not the frequency of an undisturbed body. ✗
• B. Forced: this needs an external driving force, which contradicts "undisturbed." ✗
• C. Free: "free vibration" is a term used for the motion, but the standard term for the frequency is "natural frequency." This is the closest distractor. ✗
• D. Natural: the frequency at which a body vibrates when left undisturbed. ✓
• E. Sinusoidal: describes the waveform, not the frequency. ✗

For a spring-mass system, the natural frequency is

f = (1/2π)√(k/m)

and for a simple pendulum,

f = (1/2π)√(g/L)

Both depend only on the system itself, not on any outside influence.

Answer: D, natural

Exam tip: Remember the pairing "natural frequency ↔ resonance." Resonance happens when the forced frequency equals the natural frequency. If the question says "left undisturbed" or "on its own," think natural. If it says "driven" or "external force," think forced.