Question

A block is placed on a friction less horizontal table. The mass of the block is m and springs of force constant k₁, k₂ are attached on either side with if the block is displaced a little and left to oscillate, then the angular frequency of oscillation will be

• A. $\left( \frac { k _ { 1 } + k _ { 2 } } { m } \right) ^ { 1 / 2 }$
• B. $\left[ \frac { k _ { 1 } k _ { 2 } } { m \left( k _ { 1 } + k _ { 2 } \right) } \right] ^ { 1 / 2 }$
• C. $\left[ \frac { k _ { 1 } k _ { 2 } } { \left( k _ { 1 } - k _ { 2 } \right) m } \right] ^ { 1 / 2 }$
• D. $\left[ \frac { k _ { 1 } ^ { 2 } + k _ { 2 } ^ { 2 } } { \left( k _ { 1 } + k _ { 2 } \right) m } \right] ^ { 1 / 2 }$

Answer 1

Answer: (A)

$\left( \frac { k _ { 1 } + k _ { 2 } } { m } \right) ^ { 1 / 2 }$

Answer 2

Given condition match with parallel combination so

$k _ { \text {eff } } = k _ { 1 } + k _ { 2 }$ ∴ $\omega = \sqrt { \frac { k _ { e f f } } { m } } = \sqrt { \frac { k _ { 1 } + k _ { 2 } } { m } }$ .