Two particles A and B of equal masses are suspended from two massless springs of spring constants k1 and k2, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of A and B is

Question

Two particles A and B of equal masses are suspended from two massless springs of spring constants k1 and k2, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of A and B is (A) √(k1/k2) (B) (k2/k1) (C) √(k2/k1) (D) (k1/k2)

Tardigrade Admin · Accepted Answer

Maximum velocity during SHM = Aω But k = mω2 ∴ ω = √(k/m) ∴ Maximum velocity = A√(k/m) Here the maximum velocity is same and m is also same ∴ A1√k1=A2√k2 ∴ (A1/A2)=√(k2/k1)

Q. Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_{1}$ and $k_{2}$ , respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $A$ and $B$ is

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

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

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

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

Maximum velocity during SHM = A $ω$
But k = m $ω^{2}$
$∴ ω = \frac{k}{m}$
$∴$ Maximum velocity $= A \frac{k}{m}$
Here the maximum velocity is same and m is also same
$∴ A_{1} k_{1} = A_{2} k_{2} ∴ \frac{A _{1}}{A _{2}} = \frac{k _{2}}{k _{1}}$

Q. Two particles A and B of equal masses are suspended from two massless springs of spring constants k1​ and k2​, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of A and B is

k2​k1​​​

k1​k2​​

k1​k2​​​

k2​k1​​

Maximum velocity during SHM = Aω But k = mω2 ∴ω=mk​​ ∴ Maximum velocity =Amk​​ Here the maximum velocity is same and m is also same ∴A1​k1​​=A2​k2​​∴A2​A1​​=k1​k2​​​

Q. Two particles $A$ and $B$ of equal masses are suspended from two massless springs of spring constants $k_{1}$ and $k_{2}$ , respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of $A$ and $B$ is

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

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

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

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

Maximum velocity during SHM = A $ω$
But k = m $ω^{2}$
$∴ ω = \frac{k}{m}$
$∴$ Maximum velocity $= A \frac{k}{m}$
Here the maximum velocity is same and m is also same
$∴ A_{1} k_{1} = A_{2} k_{2} ∴ \frac{A _{1}}{A _{2}} = \frac{k _{2}}{k _{1}}$