I’ve slapped together this simple VPython program to introduce sinusoidal functions to my pre-Calculus students.
- Left and right arrow keys increase and decrease the frequency;
- Up and down arrow keys increase and decrease the amplitude;
- “a” and “s” keys increase and decrease the phase.
The specific functions shown on the graph are based on the general function:
where:
- A — amplitude
- F — frequency
- P — phase
When I first introduce sinusoidal functions to my pre-Calculus students I have them make tables of the functions (from -2π to 2π with an interval of π/8) and then plot the functions. Then I’ll have them draw sets of sine functions so they can observe different frequencies, amplitudes, and phases.
from visual import *
class sin_func:
def __init__(self, x, amp=1., freq=1., phase=0.0):
self.x = x
self.amp = amp
self.freq = freq
self.phase = phase
self.curve = curve(color=color.red, x=self.x, y=self.f(x), radius=0.05)
self.label = label(pos=(xmin/2.0,ymin), text="Hi",box=False, height=30)
def f(self, x):
y = self.amp * sin(self.freq*x+self.phase)
return y
def update(self, amp, freq, phase):
self.amp = amp
self.freq = freq
self.phase = phase
self.curve.y = self.f(x)
self.label.text = self.get_eqn()
def get_eqn(self):
if self.phase == 0.0:
tphase = ""
elif (self.phase > 0):
tphase = u" + %i\u03C0/8" % int(self.phase*8.0/pi)
else:
tphase = u" - %i\u03C0/8" % int(abs(self.phase*8.0/pi))
print self.phase*8.0/pi
txt = "y = %ssin(%sx %s)" % (simplify_num(self.amp), simplify_num(self.freq), tphase)
return txt
def simplify_num(num):
if (num == 1):
snum = ""
elif (num == -1):
snum = "-"
else:
snum = str(num).split(".")[0]+" "
return snum
amp = 1.0
freq = 1.0
damp = 1.0
dfreq = 1.0
phase = 0.0
dphase = pi/8.0
xmin = -2*pi
xmax = 2*pi
dx = 0.1
ymin = -3
ymax = 3
scene.width=640
scene.height=480
xaxis = curve(pos=[(xmin,0),(xmax,0)])
yaxis = curve(pos=[(0,ymin),(0,ymax)])
x = arange(xmin, xmax, dx)
#y = f(x)
func = sin_func(x=x)
func.update(amp, freq, phase)
while 1: #theta <= 2*pi:
rate(60)
if scene.kb.keys: # is there an event waiting to be processed?
s = scene.kb.getkey() # obtain keyboard information
#print s
if s == "up":
amp += damp
if s == "down":
amp -= damp
if s == "right":
freq += dfreq
if s == "left":
freq -= dfreq
if s == "s":
phase += dphase
if s == "a":
phase -= dphase
func.update(amp, freq, phase)
#update_curve(func, y)