The time period of vertical oscillations of the system shown in figure is (. given k1=k2=k and k3=2 k )

Question

The time period of vertical oscillations of the system shown in figure is (. given k1=k2=k and k3=2 k ) (A) 2 π √(m/k) (B) 2 π √(3 m/k) (C) 2 π √(m/3 k) (D) 2 π √(2 m/3 k)

Tardigrade Admin · Accepted Answer

The spring constant of the parallel combination of springs of spring constants

k_{1}

and

k_{2}

is

k_{p} = k_{1} + k_{2} = k + k = 2 k

This combination is in series with the spring of spring constant

k_{3} .

So the effective spring constant of the system is.

\frac{1}{k _{eff}} = \frac{1}{k _{p}} + \frac{1}{k _{3}} = \frac{1}{2 k} + \frac{1}{2 k} = \frac{1}{k}

∴ k_{eff} = k

and

T = 2 π \frac{m}{k _{e ff}} = 2 π \frac{m}{k}

Q. The time period of vertical oscillations of the system shown in figure is $($ given $k_{1} = k_{2} = k$ and $k_{3} = 2 k$ )

$2 π \frac{m}{k}$

$2 π \frac{3 m}{k}$

$2 π \frac{m}{3 k}$

$2 π \frac{2 m}{3 k}$

Q. The time period of vertical oscillations of the system shown in figure is ( given k1​=k2​=k and k3​=2k )

2πkm​​

2πk3m​​

2π3km​​

2π3k2m​​

Q. The time period of vertical oscillations of the system shown in figure is $($ given $k_{1} = k_{2} = k$ and $k_{3} = 2 k$ )

$2 π \frac{m}{k}$

$2 π \frac{3 m}{k}$

$2 π \frac{m}{3 k}$

$2 π \frac{2 m}{3 k}$