# Natural Frequency Question SI Units

 P: 6 i have a basic question about the natural frequency of a system. for a mass (M), spring (k constant) undamped system the natural frequerncy is: w_n=sqrt(k/M) the units of w_n according to a lot of resources i found on the internet & textbooks are [rad/sec], my question is why? if i use the k constant units divided by the mass i get [Hz]: [k]/[M]=[N/m]/[kg]=[kg*m/s^2*m]/[kg]=[1/s^2] [w_n]=sqrt([k]/[M])=[Hz] i'll appreciate a clarification in this subject. thanks.
 P: 5,462 Hello yanaibarr, welcome to Physics Forums Radians are used because the solution to the governing differential equation is in terms of angualar measure y = Asin(x-ct) and radians (not degrees), being the natural numbers you obtain from such an expression.
Mentor
P: 12,074
 Quote by yanaibarr if i use the k constant units divided by the mass i get [Hz]: [k]/[M]=[N/m]/[kg]=[kg*m/s^2*m]/[kg]=[1/s^2] [w_n]=sqrt([k]/[M])=[Hz]
Actually you got 1/s, not Hz, for the units. You are assuming that 1/s always means Hz (= cycles/s), but that is not always the case.

Frequency can be measured in rad/s or cycles/s. Both radians and cycles are considered unitless, so both types of frequency can show up as 1/s if you use an equation to figure out the units.

Yes, but 1/s could mean either Hz or rad/s. That was my point. The frequency calculated from the $\sqrt{k/m}$ formula has units of 1/s, but is in rad/s, not Hz.