Question

The frequency of oscillations of a mass m suspended by a spring if 1. If the length of the spring is cut to one-half, the same mass oscillates with frequency 2. The value 2/ U 1 is

• A. 2
• B. $\sqrt { 2 }$
• C. 4
• D. $\sqrt { 3 }$

Answer 1

Answer: (B)

$\sqrt { 2 }$

Answer 2

The frequency of oscillations of mass m and force constant k is

$v _ { 1 } = \frac { 1 } { 2 \pi } \sqrt { \frac { k } { m } }$

When the spring is cut to one half of its length, its force constant is doubled (2k)

Then frequency of oscillation of mass m will be

$\mathrm { v } _ { 2 } = \frac { 1 } { 2 \pi } \sqrt { \frac { 2 \mathrm { k } } { \mathrm { m } } } \therefore \frac { \mathrm { v } _ { 1 } } { \mathrm { v } _ { 2 } } = \sqrt { 2 }$