The frequency of oscillation of system shown in the figure will be

Question

The frequency of oscillation of system shown in the figure will be (A) (1/2 π) √(k/M) (B) (1/2 π) √(2 k/5 M) (C) (1/2 π) √(k/5 M) (D) (1/2 π) √(2 k/M)

Tardigrade Admin · Accepted Answer

Upper two springs are in series.
Therefore, their resultant spring constant

\frac{1}{k}

,

= \frac{1}{k} + \frac{1}{k} = \frac{2}{k}

∴ k^{'} = \frac{k}{2}

Lower two springs are in parallel.
Therefore their resultant spring constant,

k^{''} = k + k = 2 k

Now, springs of constant

k^{'}

and

k^{''}

are in series.
Therefore, their resultant spring constant

\frac{1}{k _{1}} = \frac{2}{k} + \frac{1}{2 k} = \frac{4 + 1}{2 k}

k_{1} = \frac{2 k}{5}

∴

Frequency of oscillation

f = \frac{1}{T} = \frac{1}{2 π} \frac{k _{1}}{M}

= \frac{1}{2 π} \frac{2 k}{5 M}

Q. The frequency of oscillation of system shown in the figure will be

$\frac{1}{2 π} \frac{k}{M}$

$\frac{1}{2 π} \frac{2 k}{5 M}$

$\frac{1}{2 π} \frac{k}{5 M}$

$\frac{1}{2 π} \frac{2 k}{M}$

Q. The frequency of oscillation of system shown in the figure will be

2π1​Mk​​

2π1​5M2k​​

2π1​5Mk​​

2π1​M2k​​

$\frac{1}{2 π} \frac{k}{M}$

$\frac{1}{2 π} \frac{2 k}{5 M}$

$\frac{1}{2 π} \frac{k}{5 M}$

$\frac{1}{2 π} \frac{2 k}{M}$