x₁=Asin(ωt₁+φ)
v₁=ωAcos(ωt₁+φ)
sin²(ωt₁+φ)+cos²(ωt₁+φ)=1=>x₁²/A²+v₁²/ω²A²=1 (1)
analog pentru x₂=Asin(ωt₂+φ) si v₂=ωAcos(ωt₂+φ)=>x₂²/A²+v₂²/ω²A²=1 (2)
Din(1) si (2)=>A=√[(x₁²v₂²-x₂²v₁²)/(v₂²-v₁²)]=√[(3²*12²-4²*16²)/(12²-16²)]=√[(1296-4096)/(-112)]=√(2800/112)=√25=5 cm=0,05 m
Din (1) si (2)=>ω=√[(v₂²-v₁²)/(x₁²-x₂²)]=√[(12²-16²)/(3²-4²)]=√(112/7)=√16=4 rad/s
T=2π/ω=6,28/4=1,57 s
vmax=ωA=4*5=20 cm/s
E=mω²A²/2=1*4²*0,05²/2=8*0,0025=0,02 J
3 cm....................................16 cm/s
2 cm...................................v
v=2*16/3=10,66 cm/s
