35 / 10 : solve for the C1 C2 of mechanical vibration

Author: beachdweller

35_sympy/10_sympy.ipynb

@@ -1834,6 +1834,16 @@
     "\n"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x = sym.symbols('x')\n",
+    "\n"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -1898,6 +1908,96 @@
     "\n"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Initial conditions<br>초기조건\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x0, v0 = sym.symbols('x_0 v_0', real=True)\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Solving for the constant terms<br>상수 결정\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "eq0 = sym.Eq(result.rhs.subs({t:0}), x0)\n",
+    "eq0\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "c1, c2 = eq0.lhs.args\n",
+    "c1, c2\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "eq1 = sym.Eq(result.rhs.diff(t).subs({t:0}), v0)\n",
+    "eq1\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "c_dict = sym.solve([eq0, eq1], (c1, c2))\n",
+    "c_dict\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sym.simplify(c_dict[c1])\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sym.simplify(c_dict[c2])\n",
+    "\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},