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?

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/ 2) (B) 4 n (C)  ( n/ 4)  (D) 2n

Tardigrade Admin · Accepted Answer

n=(1/2 π) √(k/m) ; n prime=(1/2 π) √(k/4 m) ∴ n prime=n / 2

Q. 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?

$\frac{n}{2}$

$4 n$

$\frac{n}{4}$

$2 n$

$n = \frac{1}{2 π} \frac{k}{m}; n^{'} = \frac{1}{2 π} \frac{k}{4 m}$
$∴ n^{'} = n /2$

Q. 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 4m is suspended from the same spring?

2n​

4n

4n​

2n