# Ideal Spring Question [Units]

1. Oct 6, 2012

### Barrowlands

So, I'm trying to brush up on my undergrad physics, and I'm sure this is a bone-headed question, so please bear with me.

1. The problem statement, all variables and given/known data
A heavy object, when placed on a rubber pad that is to be used as a shock absorber, compresses the pad by 1cm. If the object is given a vertical tap, it will oscillate. Ignoring the damping, estimate the oscillation frequency. [The book i'm using actually gives the solution]

2. Relevant equations
x(t)=A*sin(sqrt(k/m)t+$\phi$)
ω=sqrt(k/m)
F=k|l-l0|

3. The attempt at a solution
We'll call x0 the equilibrium displacement, x0=1cm
k=spring constant of rubber
so
k(l-l0)=k*x0=mg (equilibrium)
gives us
k=(mg)/(x0)
then
ω=sqrt(k/m)
which eventually solves to
ω=sqrt(g/x0)

The book gives an answer of sqrt(980) rad/s. My question is given the units from ω=sqrt(g/x0) (meters, seconds, centimeters), how do they arrive at radians?

2. Oct 6, 2012

### ehild

X0 is 0.01 m. So the unit of sqrt(g/x0) is 1/s.
ω is the angular frequency, it is measured in radians/second, but radian is dimensionless. ω=2πf (f=frequency).

ehild

3. Oct 6, 2012

### Barrowlands

Makes sense. I actually just beefed the algebra cancelling my units. Thanks!