The equation of the motion of a body suspended by a spring is T=2π√m/k, where T is the time period, m is the mass of the body, and k is the force constant of spring. use this information to find the time period if a body of mass 10 kg is suspended by a spring of force constant 1400 Nm^-1. Round to the nearest tenth.
My answer: I did not exactly complete the problem as I am unsure if these values belong there; T=2π√10/1400, is this the correct step or was I supposed to convert the nanometers to a different unit?
Thank You
Nm-1 is not nanometers, it is force/distance or N/m
remember hookes law
F=kx or k=force/distance=N/m
To find the time period (T) using the equation T = 2π√(m/k), where m is the mass and k is the force constant of the spring, you have the correct formula. However, you made a small mistake in the calculation.
To solve the equation T = 2π√(m/k) for the given values of m = 10 kg and k = 1400 Nm^-1, you need to substitute these values into the formula and calculate the result.
T = 2π√(10/1400)
Now, divide 10 by 1400:
T = 2π√(0.0071)
To get the square root, calculate:
T = 2π * 0.084
Finally, multiply 2π by 0.084:
T ≈ 0.529 seconds to the nearest tenth.
Thus, the time period (T) for a body with a mass of 10 kg suspended by a spring with a force constant of 1400 Nm^-1 is approximately 0.529 seconds when rounded to the nearest tenth.