SHMHard
Question
A particle moves in x-y plane according to rule x = a sin ωt and y = a cos ωt. The particle follows
Options
A.an elliptical path
B.a circular path
C.a parabolic path
D.a straight line path inclined equally to x and y axis
Solution
x = a sin ωt or 
= sin ωt
y = a cosωt or
= cos ωt
Squaring and adding, we get
(∵ cos2 ωt + sin2 ωt = 1)
or x2 + y2 = a2
this is the equation of a circle. Hence particle follows a circular path.
= sin ωty = a cosωt or
= cos ωt Squaring and adding, we get
(∵ cos2 ωt + sin2 ωt = 1) or x2 + y2 = a2
this is the equation of a circle. Hence particle follows a circular path.
Create a free account to view solution
View Solution FreeMore SHM Questions
How long after the beginning of motion is the displacement of a harmonically oscillating particle equal to one half its ...The angle made by the string of a simple pendulum with the vertical depends upon time as θ = sin π. find the l...The distance between the point of suspension and the centre of gravity of a compound pendulum is l and the radius of gyr...Three simple harmonic motion in the same direction having the same amplitude and same period are suspended. If each diff...Two springs, each of spring constant k, are attached to a block of mass m as shown in the figure. The block can slide sm...