Oscillations
December 8, 2016
Categorised in: 12th Physics
(1) F = -kx
(2) $k = m w^2$
(3) ${d^2 x}/{dt^2} + x w^2 = 0$
(4) $PE = 1/2 k x^2$
(5) $TE = 1/2 k a^2$ = $1/2 m w^2 a^2$ = $1/2 m (2πf)^2 a^2$
(6) Composition of SHM
$x_{1} = a_{1} sin(wt + α_{1}) $
$x_{2} = a_{2} sin(wt + α_{2})$
x = R sin (wt + d)
(7) $R = √{a_1_^2 + a_2_^2 + 2a_1 a_2 cos(α_{1} – α_{2})}$
(8)Simple Pendulum: $θ = x/L$ x -> arc length
acceleration = $F/m$ = -${gx}/{L}$
$T = 2π √{{L}/{g}}$ Therefore, $w^2 = g/L$
(9) Resultant amplitude: $√{a^2 + b^2}$ & phase: $tan^{-1} (b/a)$
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