The general formula for sine wave is given as:
y = A sin (w x) + B
where,
y = height of the ladybug
A = is the amplitude of the wave or the highest peak
w = the angular frequency = 2 π f
x = seconds after landing
B = y intercept of the function
A. The A in the function refers to how high and how low
the wheels turn. So it has a maximum value of 7 in the top and also 7 in the
bottom. The negative sign simply means that the wheel starts going down first
rather than going up (classic sine is the reverse). Therefore the diameter of
the wheel is:
diameter = maximum top + maximum bottom
diameter = 7 + 7 = 14 cm
B. From the equation,
w = 2 π f = 0.4 π
Calculating for frequency f,
f = 0.2 rev / s
The period p it takes to make one revolution is the
reciprocal of f:
p = 1 / 0.2
p = 5 seconds
C. From B, it takes 5 seconds to complete 1 revolution
and in 1 revolution there is 360°. Therefore:
degrees in 1 seconds = 360° / 5 seconds = 72° / 1 second
Hence, the ladybug turns 72° in 1 second.
D. The value of B gives the initial height of the
ladybug. Therefore the minimum and maximum heights is:
h = B ± diameter
h = 11 ± 7
h = 4, 18
Hence the min height is 4 cm and max height is 18 cm
above the ground.
E. Simply plug in x = 3
y = -7 sin(0.4π*3) + 11
y = -0.46 + 11
y = 10.54 cm above the ground
