Question

1.Un pendul gravitational de lungime l=1 m oscileaza fara frecarr cu aerul.
Determinati perioada si frecventa pendulului.
2.Un pendul gravitational oscileaza cu frecventa V=4 Hz. Determinati lungimea pendulului 1/4. g=10 N/kg
Va rog ajutati-ma!

Answer 1

O sa consider ca suntem in conditii de izocronism.

$1. T=2\pi \sqrt{\dfrac{l}{g}}\\T=2\cdot \sqrt{\pi^2\cdot \dfrac{1}{g}}\\\text{Putem simplifica }\pi^2 \text{ cu }g.\\T=2\sqrt 1= 2 s\\\nu =\dfrac{1}{T}\\\nu = \dfrac{1}{2}=  0,5\ Hz$

$2. T=\dfrac{1}{\nu }\\T=\dfrac{1}{4} =0,25 s\\T=2\cdot \pi \sqrt{\dfrac{l}{g}}|()^2\\T^2=4\pi^2 \cdot \dfrac{l}{g}\\\text{Din nou putem simplifica }\pi^2 \text{ cu }g.\\T^2=4l\\l=\dfrac{T^2}{4}\\l=\dfrac{0,0625}{4}=0,015625 m$