diff --git a/Checkpoints/Checkpoint3.ipynb b/Checkpoints/Checkpoint3.ipynb index 4ac9de2e24e6d2b62a05643037998f4318c631cc..6c973dda1cba03cff54ad2ac9342171a6a847fb4 100644 --- a/Checkpoints/Checkpoint3.ipynb +++ b/Checkpoints/Checkpoint3.ipynb @@ -29,11 +29,11 @@ "\n", "The solutions to this equation take the following forms:\n", "\n", - "$$ x=\\exp(−γt/2)[a\\cosh(pt)+b\\sinh(pt)] when γ>2ω_0 with p^2=(γ^2/4)−ω^2_0 $$\n", + "$$ x=\\exp(−γt/2)[a\\cosh(pt)+b\\sinh(pt)] \\text{when} γ>2ω_0 \\text{with} p^2=(γ^2/4)−ω^2_0 $$\n", "\n", - "$$ x=\\exp(−γt/2)[a+bt] when γ=2ω_0 $$\n", + "$$ x=\\exp(−γt/2)[a+bt] \\text{when} γ=2ω_0 $$\n", "\n", - "$$ x=\\exp(−γt/2)[a\\cos(ωt)+b\\sin(ωt)] when γ<2ω_0 with ω^2=ω^2_0−(γ^2/4)$$\n", + "$$ x=\\exp(−γt/2)[a\\cos(ωt)+b\\sin(ωt)] \\text{when} γ<2ω_0 \\text{with} ω^2=ω^2_0−(γ^2/4)$$\n", "\n", "where these three conditions are known as over damped, critically damped and under damped respectively.\n", "\n", @@ -41,11 +41,11 @@ "\n", "With the initial conditions that x=1 and $\\dot{x}$ =0 at t=0 the above constants, after some manipulation, become,\n", "\n", - "a=1 b=$\\gamma$/2p when $\\gamma$>2ω$_0$\n", + "a=1 $b=\\gamma/2p$ when $\\gamma$>2ω$_0$\n", "\n", - "a=1 b=$\\gamma$/2 when $\\gamma$=2ω$_0$\n", + "a=1 $b=\\gamma/2$ when $\\gamma$=2ω$_0$\n", "\n", - "a=1 b=$\\gamma$/2ω when $\\gamma$<2ω$_0$\n", + "a=1 $b=\\gamma/2ω$ when $\\gamma$<2ω$_0$\n", "\n", "### Task\n", "\n",