1Which of these has the same dimensions as damping constant?
Damping constant and mass flow rate both have the dimensions [M T⁻¹].
Oscillations and wavesClass 11, Oscillations
Dimensional formula of Damping constant
[M T-1]
The constant in the damping force F = -bv. It is force per unit velocity.
How to get the dimensional formula of damping constant
- Start from the definition: damping constant = force / velocity.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- acceleration = velocity / time, so acceleration is [L T-1] / [T] = [L T-2].
- force = mass × acceleration, so force is [M] × [L T-2] = [M L T-2].
- Put in the dimension of each part: [M L T-2] / [L T-1].
- Add the powers of each base quantity: [M T-1].
Quantities with the dimensions [M T⁻¹]
Equal dimensions do not make them the same quantity. Compare damping constant with the others in the full grid.
Three questions on damping constant
2What is the SI unit of damping constant?
The SI unit of damping constant is the kilogram per second (kg/s).
3Do damping constant and intensity of a wave have the same dimensions?
Damping constant is [M T⁻¹] but intensity of a wave is [M T⁻³].
Damping constant: quick answers
What is the dimensional formula of damping constant?
The dimensional formula of damping constant is [M T⁻¹]. It comes from damping constant = force / velocity.
What is the SI unit of damping constant?
The SI unit of damping constant is the kilogram per second (kg/s).
Which quantities have the same dimensions as damping constant?
Damping constant shares [M T⁻¹] with mass flow rate. Equal dimensions do not make them the same quantity.