A .436 kg mass is attached to a spring and executes simple harmonic motion with a period of .19s. The total energy of the system is 4.6 J.
find force constant of the spring.
Answer in units of N/m
To find the force constant of the spring, we need to understand the relationship between the period of a mass-spring system and the force constant.
The period (T) of an object undergoing simple harmonic motion with a mass (m) attached to a spring is related to the force constant (k) by the formula:
T = 2π√(m/k)
where π is approximately equal to 3.14159.
In this case, we are given the period (T) as 0.19 seconds, and the mass (m) as 0.436 kg. We need to find the force constant (k).
Let's rearrange the formula to solve for the force constant:
T = 2π√(m/k)
Rewriting the formula:
k = (4π^2m) / T^2
Substituting the given values:
k = (4 * 3.14159^2 * 0.436) / 0.19^2
Evaluating the expression using a calculator:
k ≈ 276.67 N/m
Therefore, the force constant of the spring is approximately 276.67 N/m.