Question

Un oscilator liniar armonic cu masa de 5 kg oscileaza dupa ecuatia y=10sin(∏t-∏) (m)
sa se afle:amplitudinea,viteza,aceleratia

Answer 1

Răspuns:

y= 10*sin(πt-π) (m)

st ca y= A* sin( ωt+ γ₀)  

=> A= 10 m, ω= π s⁻¹ , γ₀= -π rad

v= ωA*sin(ωt+γ₀+ π/2)

v= 10π*sin(πt-π+π/2)

v= 10π* sin(πt-π/2) = 10π * sin( -(π/2-πt) )= -10π* sin(π/2-πt) = -10π*cos πt  (m/s)

a= ω²A* sin(ωt+γ₀+ π)

a=10* π²* sin( πt- π+π) = 10*10* sin(πt)= 100*sin(πt) (m/s²)

obs. π² ≈ 10