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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.
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]
x(t)=A*sin(sqrt(k/m)t+[itex]\phi[/itex])
ω=sqrt(k/m)
F=k|l-l0|
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?
Homework Statement
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]
Homework Equations
x(t)=A*sin(sqrt(k/m)t+[itex]\phi[/itex])
ω=sqrt(k/m)
F=k|l-l0|
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?