Two bodies M and N of equal masses are suspended from two separate massless springs of spring constants k1 and k2 respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitudes of vibrations of M to that of N is

Question

Two bodies M and N of equal masses are suspended from two separate massless springs of spring constants k1 and k2 respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitudes of vibrations of M to that of N is (A)  (k1/k2)  (B)  √(k1/k2)  (C)  (k2/k1)  (D)  √(k2/k1)

Tardigrade Admin · Accepted Answer

Maximum velocities are equal Hence, a1ω 1=a2ω 2 (a1/a2)=(ω 2/ω 1) =(2π text/n2/2π text/n1) =(T2/T1)=(2π √m1 text/k1/2π √m text/k2) =√(k2/k1)

Q. Two bodies M and N of equal masses are suspended from two separate massless springs of spring constants $k_{1}$ and $k_{2}$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitudes of vibrations of M to that of N is

$\frac{k _{1}}{k _{2}}$

$\frac{k _{1}}{k _{2}}$

$\frac{k _{2}}{k _{1}}$

$\frac{k _{2}}{k _{1}}$

Maximum velocities are equal Hence, $a_{1} ω_{1} = a_{2} ω_{2}$ $\frac{a _{1}}{a _{2}} = \frac{ω _{2}}{ω _{1}}$ $= \frac{2 π / n _{2}}{2 π / n _{1}}$ $= \frac{T _{2}}{T _{1}} = \frac{2 π m _{1} / k _{1}}{2 π m / k _{2}}$ $= \frac{k _{2}}{k _{1}}$

Q. Two bodies M and N of equal masses are suspended from two separate massless springs of spring constants k1​ and k2​ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitudes of vibrations of M to that of N is

k2​k1​​

k2​k1​​​

k1​k2​​

k1​k2​​​

Maximum velocities are equal Hence, a1​ω1​=a2​ω2​ a2​a1​​=ω1​ω2​​ =2π/n1​2π/n2​​ =T1​T2​​=2πm/k2​​2πm1​/k1​​​ =k1​k2​​​

Q. Two bodies M and N of equal masses are suspended from two separate massless springs of spring constants $k_{1}$ and $k_{2}$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitudes of vibrations of M to that of N is

$\frac{k _{1}}{k _{2}}$

$\frac{k _{1}}{k _{2}}$

$\frac{k _{2}}{k _{1}}$

$\frac{k _{2}}{k _{1}}$

Maximum velocities are equal Hence, $a_{1} ω_{1} = a_{2} ω_{2}$ $\frac{a _{1}}{a _{2}} = \frac{ω _{2}}{ω _{1}}$ $= \frac{2 π / n _{2}}{2 π / n _{1}}$ $= \frac{T _{2}}{T _{1}} = \frac{2 π m _{1} / k _{1}}{2 π m / k _{2}}$ $= \frac{k _{2}}{k _{1}}$