A system is shown in the figure. The time period for small oscillations of the two blocks will be

Question

A system is shown in the figure. The time period for small oscillations of the two blocks will be (A) 2 π √(3 m/k) (B) 2 π √(3 m/2 k) (C) 2 π √(3 m/4 k) (D) 2 π √(3 m/8 k)

Tardigrade Admin · Accepted Answer

Both the spring are in series ∴ K eq =(K(2 K )/K+2 K)=(2 K/3) Time period T=2 π √(μ/K eq ) where μ=(m1 m2/m1+m2) Here μ=(m/2) ∴ T=2 π √(m/2) ⋅ (3/2 K)=2 π √(3 m/4 K)

Q. A system is shown in the figure. The time period for small oscillations of the two blocks will be

$2 π \frac{3 m}{k}$

$2 π \frac{3 m}{2 k}$

$2 π \frac{3 m}{4 k}$

$2 π \frac{3 m}{8 k}$

Both the spring are in series
$∴ K_{e q} = \frac{K ( 2 K )}{K + 2 K} = \frac{2 K}{3}$
Time period
$T = 2 π \frac{μ}{K _{e q}}$ where $μ = \frac{m _{1} m _{2}}{m _{1} + m _{2}}$
Here $μ = \frac{m}{2}$
$∴ T = 2 π \frac{m}{2} \cdot \frac{3}{2 K} = 2 π \frac{3 m}{4 K}$

Q. A system is shown in the figure. The time period for small oscillations of the two blocks will be

2πk3m​​

2π2k3m​​

2π4k3m​​

2π8k3m​​

Both the spring are in series ∴Keq​=K+2KK(2K)​=32K​ Time period T=2πKeq​μ​​ where μ=m1​+m2​m1​m2​​ Here μ=2m​ ∴T=2π2m​⋅2K3​​=2π4K3m​​

$2 π \frac{3 m}{k}$

$2 π \frac{3 m}{2 k}$

$2 π \frac{3 m}{4 k}$

$2 π \frac{3 m}{8 k}$

Both the spring are in series
$∴ K_{e q} = \frac{K ( 2 K )}{K + 2 K} = \frac{2 K}{3}$
Time period
$T = 2 π \frac{μ}{K _{e q}}$ where $μ = \frac{m _{1} m _{2}}{m _{1} + m _{2}}$
Here $μ = \frac{m}{2}$
$∴ T = 2 π \frac{m}{2} \cdot \frac{3}{2 K} = 2 π \frac{3 m}{4 K}$