#### Two particles and B of equal masses are suspended from two massless springs of spring constants and respectively. If the maximum velocities, during oscillations, are equal, the ratio of amplitudes of and B is Option 1) Option 2) Option 3) Option 4)

As we learnt in

Relation of velocity and displacement -

- wherein

x is displacement from mean position

A is Amplitude.

Maximum velocity under simple harmonic motion $\dpi{100} v_{m}=a\omega$

$\dpi{100} \therefore \; \; \; v_{m}=\frac{2\pi a}{T}=(2\pi a)\left ( \frac{1}{T} \right )=(2\pi a)\left ( \frac{1}{2\pi }\sqrt{\frac{k}{m}} \right )$

$\dpi{100} or\; \; \; v_{m}=a\sqrt{\frac{k}{m}}$

$\dpi{100} \because \; \; \; (v_{m})_{A}=(v_{m})_{B}$

$\dpi{100} \therefore \; \; \; a_{1}\sqrt{\frac{k_{1}}{m}}=a_{2}\sqrt{\frac{k_{2}}{m}}\Rightarrow \frac{a_{1}}{a_{2}}=\sqrt{\frac{k_{2}}{k_{1}}}$

Correct option is 3.

Option 1)

This is an incorrect option.

Option 2)

This is an incorrect option.

Option 3)

This is the correct option.

Option 4)

This is an incorrect option.