If the time period of undamped oscillation is T and that of damped oscillation is T^', then what

Step 1: In undamped condition, the time period (T) can be written as $frac{pi}{omega}$, which is

If the time period of undamped oscillation is T and that of...

If the time period of undamped oscillation is $\mathrm{T}$ and that of damped oscillation is $\mathrm{T}^{\prime}$, then what is the relation between $\mathrm{T} \& \mathrm{~T}^{\prime}$ (A) $\mathrm{T}^{\prime}<\mathrm{T}$ (B) nothing can be said, unless the drag force constant is known. (C) $\mathrm{T}^{\prime}=\mathrm{T}$ (D) $\mathrm{T}^{\prime}>\mathrm{T}$

If the time period of undamped oscillation is $\mathrm{T}$ and that of damped oscillation is $\mathrm{T}^{\prime}$, then what is the relation between $\mathrm{T} \& \mathrm{~T}^{\prime}$
(A) $\mathrm{T}^{\prime}<\mathrm{T}$
(B) nothing can be said, unless the drag force constant is known.
(C) $\mathrm{T}^{\prime}=\mathrm{T}$
(D) $\mathrm{T}^{\prime}>\mathrm{T}$

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Key Concepts

Undamped Oscillation

Undamped oscillation refers to a system oscillating without any loss of energy due to friction or resistance. In such systems, once set into motion, the oscillations continue indefinitely with a constant amplitude and a natural angular frequency, which is determined solely by the system's intrinsic properties.

Damped Oscillation

Damped oscillation occurs when a resisting force, such as friction or air resistance, acts on an oscillating system, causing the amplitude to gradually decrease over time. Although the amplitude decays, the system continues to oscillate with an angular frequency that is different from its undamped natural frequency due to the energy loss.

Effect of Damping on Oscillation Period

The presence of damping alters the effective angular frequency of an oscillatory system. The damped angular frequency is lower than the natural undamped angular frequency because some energy is dissipated in each cycle. Consequently, the period of oscillation in a damped system is longer than that in an undamped system, meaning that damping leads to a slower oscillation.

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