A system consist of two springs and a mass m=1 kg 𝑚=1 kg as shown in figure. If mass m is displaced slightly along vertical and released, the system oscillates with a period of 2s. Then the spring constant k is
Question
A system consist of two springs and a mass m=1 kg 𝑚=1 kg as shown in figure. If mass m is displaced slightly along vertical and released, the system oscillates with a period of 2s. Then the spring constant k is
Solution
The period of oscillation for a spring-mass system is given by the formula:
T = 2π√(m/k)
where: T is the period, m is the mass, and k is the spring constant.
We can rearrange this formula to solve for k:
k = m / (T/(2π))^2
Given that m = 1 kg and T = 2 s, we can substitute these values into the formula:
k = 1 / (2/(2π))^2
Solving this gives:
k = (1 / (1/π^2)) = π^2 N/m
So, the spring constant k is approximately 9.87 N/m.
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