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 [tex]T = 2pi\sqrt{\frac{m}{k} }[/tex]
[tex]\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} [/tex]
