Two identical particles each of mass m are interconnected by a light spring of stiffness k, the time period for small oscillation is equal to

Question

Two identical particles each of mass m are interconnected by a light spring of stiffness k, the time period for small oscillation is equal to (A) 2 π √(m/k) (B) (π/2) √(m/k) (C) π √(m/2 k) (D) π √(2 m/k)

Tardigrade Admin · Accepted Answer

The reduced mass μ=((m)(m)/m+m)=(m/2) The given system is equivalent to a system of a particle of mass m / 2 connected to a spring of stiffness k rigidly. The required period of oscillation. T =2 π √(μ/k)=2 π √(m / 2/k) =π √(2 m/k)

Q. Two identical particles each of mass $m$ are interconnected by a light spring of stiffness $k$ , the time period for small oscillation is equal to

$2 π \frac{m}{k}$

$\frac{π}{2} \frac{m}{k}$

$π \frac{m}{2 k}$

$π \frac{2 m}{k}$

The reduced mass
$μ = \frac{( m ) ( m )}{m + m} = \frac{m}{2}$
The given system is equivalent to a system of a particle of mass $m /2$ connected to a spring of stiffness $k$ rigidly.
The required period of oscillation.
$T = 2 π \frac{μ}{k} = 2 π \frac{m /2}{k}$
$= π \frac{2 m}{k}$

Q. Two identical particles each of mass m are interconnected by a light spring of stiffness k, the time period for small oscillation is equal to

2πkm​​

2π​km​​

π2km​​

πk2m​​