- #1
Rae
- 2
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Summary: How to express ωₙ in terms of only mass (m) and stiffness (k)? I tried doing it with F=kx but it is out of my ability to simplify it to only m and k.
Here is my approach:
Here is my approach:
From what i was taught in my lecture classes, ##\delta_{st}## means the initial displacement that the spring has before we displace it further by x. I am not sure if it is needed in this case.hutchphd said:Tell me what is ##\delta_{st}##?
You need (a free body diagram and) Newton's law for each mass, and the constraint on the positions (and hence accelerations) engendered by the pulley system.
The formula for calculating natural frequency is ωₙ = √(k/m), where k is the stiffness and m is the mass.
To express ωₙ in terms of only mass and stiffness, you can use the formula ωₙ = √(k/m).
Yes, you can use any units for mass and stiffness as long as they are consistent. For example, if you use kilograms for mass, you should use newtons per meter for stiffness.
Yes, the unit for natural frequency is radians per second (rad/s).
Increasing the mass will decrease the natural frequency, while increasing the stiffness will increase the natural frequency. This is because the natural frequency is inversely proportional to the square root of the mass, and directly proportional to the square root of the stiffness.