Question

a mass of 0.30kg is attached to a spring and is set in motion with a period of 0.24 s. what is the spring constantof the spring ​

Answer 1

Answer:

The spring constant of the spring is 205.42 N/m.

Explanation:

Springs have their own natural "spring constants" that define how stiff they are. The letter k is used for the spring constant, and it has the units N/m.

                                                          k = -F/x

The period of a spring-mass system is proportional to the square root of the mass and inversely proportional to the square root of the spring constant.

Given:

mass of object in SHM = m = 0.30 kg

Time period of the spring mass system = 0.24s

Spring constant = k ?

Finding 'k' using Time period 'T':

We know that $T = 2pi\sqrt{\frac{m}{k} }$

$\frac{T}{2pi} = \sqrt{\frac{m}{k} }\\ \frac{T^{2} }{4(3.14)^{2} } = \frac{m}{k}\\ k = \frac{m*4*9.86}{T^{2} } \\k = \frac{0.3*4*9.86}{0.24^{2}}\\k = 205.42 N/m}$