If the maximum velocity of two springs (both has same mass)...

If the maximum velocity of two springs (both has same mass) executing S.H.M. and having force constants $\mathrm{k}_{1}$ and $\mathrm{k}_{2}$ respectively are same, then the ratio of their amplitudes will be $\ldots \ldots$ (A) $\left(\mathrm{k}_{1} / \mathrm{k}_{2}\right)$ (B) $\left(\mathrm{k}_{2} / \mathrm{k}_{1}\right)$ (C) $\sqrt{\left(k_{1} / k_{2}\right)}$ (D) $\sqrt{\left(k_{2} / k_{1}\right)}$

If the maximum velocity of two springs (both has same mass) executing S.H.M. and having force constants $\mathrm{k}_{1}$ and $\mathrm{k}_{2}$ respectively are same, then the ratio of their amplitudes will be $\ldots \ldots$
(A) $\left(\mathrm{k}_{1} / \mathrm{k}_{2}\right)$
(B) $\left(\mathrm{k}_{2} / \mathrm{k}_{1}\right)$
(C) $\sqrt{\left(k_{1} / k_{2}\right)}$
(D) $\sqrt{\left(k_{2} / k_{1}\right)}$

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Key Concepts

Simple Harmonic Motion (SHM)

SHM is a type of oscillatory motion where the restoring force is directly proportional to the displacement from the equilibrium position and acts in the direction opposite to the displacement. This concept forms the foundation for understanding the dynamics of systems like mass-spring oscillators.

Angular Frequency in Mass-Spring Systems

For a mass-spring system, the angular frequency (?) is defined as ? = ?(k/m), where k is the spring's force constant and m is the mass attached to the spring. This relationship highlights how the stiffness of the spring influences the rate of oscillation.

Maximum Velocity in SHM

In SHM, the maximum velocity is reached as the object passes through the equilibrium position and is given by v_max = A?, where A is the amplitude and ? is the angular frequency. This relationship is critical when comparing systems with equal maximum velocities to determine other related parameters like amplitude.

Amplitude

Amplitude represents the maximum displacement from the equilibrium position in an oscillatory system. Given its direct relationship with the maximum velocity in SHM, when the maximum velocities are equal between two oscillators with different spring constants, differences in amplitude compensate for the variations in angular frequency.

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