TRP_ Archimedean Spiral

A parametric equation of the ARCHIMEDEAN spiral has been traced. It is seen in nature https://www.google.co.in/search?q=archimedean+spiral+found+in+nature&espv=2&biw=1366&bih=667&tbm=isch&tbo=u&source=univ&sa=X&ei=zDQIVZujCcThuQSF04LQDA&ved=0CDUQsAQ&dpr=1 you can move the three SLIDERS to experience the changes..magnitudes and the phases and the no of loops can be very easily manipulated...enjoy !!!
1. Enlist the parametric equation of this spiral. 2. WAVE shaping Theory is one of the subjects where an engineering student can find its direct application.. 3. Also as an exercise , try finding out the various types of SPIRALS which exist in NATURE and their mathematical equations, polar or Parametric. 4. Try using ANY software to TRACE them !!!