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--- repository:cat_toy [2020/04/02 00:46]
porcaro1 [Cat Toy]
+++ repository:cat_toy [2020/04/02 00:57]
porcaro1 [Cat Toy]
@@ Line 50: / Line 50: @@
   - Modify the code above to get your system to behave as an ideal simple harmonic oscillator. Ignore external forces such as gravity.
   - Plot the potential, kinetic, and total energy of the mass-spring system as they relate to time (hint: use the plot command in GlowScript).
-  - (Optional 1): Add a linear damping effect to your system with a damping coefficient (c).
+  - (Optional 1): Add a linear damping effect to your system with a damping coefficient "c".
   - (Optional 2): Make your system into a vertical mass-spring system and include the force of gravity in your calculations.
 {{ :repository:cattoy.png?nolink|}}
 ===Working Code===
+**Horizontal Spring (with Optional Linear Damping)**
 <code Python [enable_line_numbers="true", highlight_lines_extra="0"]>
 GlowScript 2.7 VPython
@@ Line 90: / Line 92: @@
 t = 0
 dt = 0.001
 while t < t_final:
@@ Line 118: / Line 119: @@
     t = t + dt </code>
+**Vertical Spring with Gravity**
+<code Python [enable_line_numbers="true", highlight_lines_extra="0"]>
+GlowScript 2.7 VPython
+#System parameters: Length of spring at equilibrium (L0), spring constant (k), damping constant (c)
+g = 10
+mBlock = 0.3
+L0 = 5
+k = 500
+c = 0.3
+#Objects: track, wall, block, and spring
+#track = box(pos = vec(0,0,0), size = vec(10,0.1,2), color = color.gray(0.7))
+wall = box(pos = vec(0,5,0), size = vec(3,0.5,3), color = color.gray(0.7))
+block = box(pos = vec(0,2.5,0), size = vec(2,2,2), color = color.red)
+spring = helix(pos = wall.pos, size = vec(mag(block.pos-wall.pos),0.75,0.75), axis = block.pos-wall.pos, color = color.red)
+spring.thickness = 0.1 #Spring thickness attribute
+#Initializing system variables: Length of spring (L), length unit vector (Lhat), and stretch or displacement from equilibrium (s)
+L = block.pos - spring.pos
+Lhat = L/mag(L)
+s = mag(L) - L0
+#Initializing empty force vectors
+Fspring = vec(0,0,0)
+Fdamp = vec(0,0,0)
+Fgrav = vec(0,0,0)
+Fnet = vec(0,0,0)
+#Block attributes
+block.mass = mBlock
+block.p = vec(0,0,0)
+#Initialize data series for U, K, and E graphs. http://www.glowscript.org/docs/GlowScriptDocs/graph.html
+Ugraph = series(color=color.green)
+Kgraph = series(color=color.red)
+Egraph = series(color=color.blue)
+#Time and time step
+t = 0
+dt = 0.00005
+#Trigger for program to begin with mouse click
+print("Click the program window to begin.")
+ev = scene.waitfor('click')
+print("The program is running.")
+#Begin update loop
+while t<10:
+    rate(5000)
+    L = block.pos - spring.pos
+    Lhat = L/mag(L)
+    s = mag(L) - L0
+    Fspring = -1*k*s*Lhat
+    Fdamp = -1*c*block.p/block.mass
+    Fgrav = block.mass*vec(0,-g,0)
+    Fnet = Fspring+Fdamp+Fgrav
+    block.p = block.p + Fnet*dt
+    block.pos = block.pos + block.p/block.mass*dt
+    spring.axis = Lhat
+    spring.size = vec(mag(L),0.75,0.75)
+    U = 0.5*k*s**2
+    K = 0.5*block.mass*mag(block.p/block.mass)**2
+    E = U + K
+    Ugraph.plot(t,U)
+    Kgraph.plot(t,K)
+    Egraph.plot(t,E)
+    t = t + dt
+print("the program is complete.")</code>
 ===Debrief Questions===
   - What challenges do you anticipate facing when teaching a problem like this? What challenges do you anticipate your students facing when working on a problem like this?