Question

5. A mass 4 kg is suspended from spring of constant K and put into oscillation. If time period is
seconds constant of spring K is
1) 12.5 N/m
2) 30 N/m
3) 5 N/m
4) 25 N/m
​

Answer 1

a mass 4 kg is suspended fr spring of constant k and put into oscillation

Explanation:

12.5 N/m

Answer 2

Step by step explanation:

Given :  A mass 4 kg is suspended from spring of constant K and put into oscillation. If time period is 4π/5 seconds.

To find : Spring constant (K)

Formula used :

   $T=2\pi \sqrt{\frac{M}{K} }$

T is the time period of oscillation, M is the mass of object and K is the spring constant.

Calculation for spring constant (K) :

We are given with the mass of object(M) = 4 Kg and

time period (T) = 4π/5 sec

By using formula we can write,

⇒  $T=2\pi \sqrt{\frac{M}{K} }$

⇒  $\frac{4\pi}{5}=2\pi \sqrt{\frac{4}{K} }$

taking 2π to the other side,

⇒  $\frac{4\pi}{5}*\frac{1}{2\pi} = \sqrt{\frac{4}{K} }$

⇒  $\frac{2}{5} =\sqrt{\frac{4}{K} }$

Squaring on both sides,

⇒  $({\frac{2}{5}})^{2} =(\sqrt{\frac{4}{K} } )^{2}$

⇒  $\frac{4}{25} =\frac{4}{K}$

rearranging the fractions and find the value of K,

⇒  $K=\frac{4*25}{4}$

⇒  K = 25 N/m

Hence we get the spring constant as 4) 25 N/m.

and complete question is,

Ques - A mass 4 kg is suspended from spring of constant K and put into oscillation. If time period is 2π/5 seconds constant of spring K is

1) 12.5 N/m

2) 30 N/m

3) 5 N/m

4) 25 N/m