A mass oscillates with a period of 2.8 s on the end of a spring that has a spring constant of 75 N/m. What is the magnitude of the mass?
T =2•π•sqrt(m/k),
m = T²•k/4•π² =2.8²•75/4•π² =14.9 kg.
yeah you just do it
To find the magnitude of the mass, we can use the formula for the period of a mass-spring system:
T = 2π √(m/k)
Where T is the period, m is the mass, and k is the spring constant.
Given that the period T is 2.8 s and the spring constant k is 75 N/m, we can rearrange the formula to solve for the mass m:
T = 2π √(m/k)
Square both sides of the equation to get rid of the square root:
T^2 = (2π)^2 (m/k)
Now, isolate m by multiplying both sides of the equation by k:
kT^2 = (2π)^2 m
Divide both sides of the equation by (2π)^2 to solve for m:
m = kT^2 / (2π)^2
Plugging in the values for k = 75 N/m and T = 2.8 s, we can calculate the magnitude of the mass m:
m = (75 N/m) * (2.8 s)^2 / (2π)^2
m ≈ 5.061 kg
Therefore, the magnitude of the mass is approximately 5.061 kg.
To find the magnitude of the mass, we can use the formula for the period of a mass-spring system, which is given by:
T = 2π√(m/k)
where T is the period, m is the mass, and k is the spring constant.
In this case, we are given that the period T is 2.8 s and the spring constant k is 75 N/m.
Rearranging the formula, we get:
m = (T / (2π))^2 * k
Plugging in the values:
m = (2.8 / (2π))^2 * 75
Calculating this expression, we find:
m = 0.3943 * 75
m ≈ 29.58 kg
Therefore, the magnitude of the mass is approximately 29.58 kg.