VDU_Physics_2_003  
Solved UniversityPhysics ProblemsPhysics 2. Lissajous PatternsJavier Montenegro Joo
jmj@VirtualDynamics.Org


Lissajous Patterns 

(1)
A
particle is attached to two perpendicular springs oscillating on the
plane XY, with SHMs given by X = A Cos( wt ) and Y
= B Cos( wt – p ) , respectively.
Construct and identify the equation of motion of the particle for
the case when p = 90^{o }
Solution.




(2) Two perpendicular springs vibrate according to the equations below. Determine the curve described by a small ball attached to the extremes of both oscillators.
Solution. It can be seen that the angular frequencies are equal and that the difference between initial phases is Pi:




(3) Two oscillators vibrate according to:
Determine the curve that results when x1 is graphed against x2. Solution. It can be seen that the angular velocities of both oscillators is the same and that the difference between initial phases is Pi/2:


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(4) A little ball displaces attached to two perpendicular coil springs which vibrate according to x(t) and y(t) given below. Construct and identify the orbit described by the little ball.
Solution.




(5) A small ball oscillates attached to the extremes of two perpendicular springs which oscillate according to the equations and conditions shown below. Determine the orbits described by the small ball when the oscillation amplitudes are: (a) different (b) when they are equal to each other.
Solution.


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