Question

A particle moves in the X-Y plane according to the equation
r = (i+2j)A.cos⍵t.
The motion of the particle is
(a) on a straight line
(b) on an ellipse
(c) periodic
(d) simple harmonic

Answer 1

Given Equation of the Simple Harmonic Motion,

 r = (i + 2j)ACoswt

i + 2j is showing the direction of the of the Particle in a straight line.

Hence, the Motion is a straight line motion. Therefore, Option (a). is correct.

Now,

Except the direction mentioned which is showing straight line nature, rest of the equation is same as that of the S.H.M. , y = ACoswt, therefore it is S.H.M.

Now, Since, it is S.H.M. , therefore it is Oscillatory and Periodic Motion.

Hence, option (a), (c) and (d) are correct.

Hope it helps.

Answer 2

Given Equation of the Simple Harmonic Motion,

 r = (i + 2j)ACoswt

i + 2j is showing the direction of the of the Particle in a straight line.

Hence, the Motion is a straight line motion. Therefore, Option (a). is correct.

Now,

Except the direction mentioned which is showing straight line nature, rest of the equation is same as that of the S.H.M. , y = ACoswt, therefore it is S.H.M.

Now, Since, it is S.H.M. , therefore it is Oscillatory and Periodic Motion.

Hence, option (a), (c) and (d) are correct.