Question

A mass m is vertically suspended from a spring of negligible mass; the system oscillates with a frequency n. What will be the frequency of the system if a mass 4 m is suspended from the same spring

• A. $n / 4$
• B. $4 n$
• C. $n / 2$
• D. $2 n$

Answer 1

Answer: (C)

$n / 2$

Answer 2

$n = \frac { 1 } { 2 \pi } \sqrt { \frac { k } { m } } \Rightarrow n \propto \frac { 1 } { \sqrt { m } } \Rightarrow \frac { n _ { 1 } } { n _ { 2 } } = \sqrt { \frac { m _ { 2 } } { m _ { 1 } } }$

$\Rightarrow \frac { n } { n _ { 2 } } = \sqrt { \frac { 4 m } { m } } \Rightarrow n _ { 2 } = \frac { n } { 2 }$