Physics(Oscillation)?

Question

I don't know the terms in english but I'll try to explain though....

The information is:
The corp's weight(m)=0.01 Kg
The distance of the corp's oscillation(not the full distance)(Y)=1/2 of the full distance which the corp could reach during the oscillation
Corp's speed(v)=0.17/s
Acceleration(a)=0.07m/s^2

- Whch is the frequency(F)?
- Which is the full distance(A) which the corp reaches during it's oscillation?

thanks ;)

Answer 1

In harmonic (sinusoidal) oscillation, the instantaneous position (x), velocity (v) and acceleration (a) are successive derivatives and are related by the natural frequency ω and trigonometry to the position amplitude A as follows:
x = Asin(ωt); v = ω*Acos(ωt); a = -ω^2*Asin(ωt)
From your question I understand that the data given are at a time t when x = 0.5A. So ωt = arcsin(0.5). From the equations for v and a you can compute ωA = v/cos(ωt) and ω^2A = a/sin(ωt) (the - sign is ignored since it was ignored in the data*). From these you can solve for ω, A and F.
*If x is positive, a is negative.