A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x-2 -160-sin -160- -969-t- -160- -160- -160- -160- -160-y-2 -160-sin -160- -969-t- -960-4-The path of the particle will be-a- a straight line nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- -b- a circle nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- -c- an ellipse nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- nbsp- -d- a parabola

Dear Student , As the phase difference is constant that is nbsp; #981;= #960;4 nbsp;. So the resultant path of the particle will be an ellipse . Here ...

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Standard XII

Mathematics

Properties of Determinants

A particle is...

Question

A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by $x = 2 \sin ω t : y = 2 \sin (ω t + \frac{π}{4})$
The path of the particle will be
(a) a straight line (b) a circle (c) an ellipse (d) a parabola

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Solution

Dear Student ,
As the phase difference is constant that is $ϕ = \frac{π}{4}$ . So the resultant path of the particle will be an ellipse .
$H e r e x = \sin ω t a n d y = \cos (ω t + \frac{π}{4}) S o s q u a r i n g a n d a d d i n g b o t h s i d e s w e c a n w r i t e t h a t, x^{2} + \frac{y^{2}}{4} = 1 S o t h e p a t h w i l l b e e l l i p s e .$
Regards

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A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by x=2 sin ωt: y=2 sin ωt+π4 The path of the particle will be (a) a straight line (b) a circle (c) an ellipse (d) a parabola

Dear Student , As the phase difference is constant that is ϕ=π4 . So the resultant path of the particle will be an ellipse . Here x=sinωt and y =cosωt+π4So squaring and adding both sides we can write that ,x2+y24=1So the path will be ellipse . Regards

A particle is subjected to two mutually perpendicular simple harmonic motions such that its x and y coordinates are given by $x = 2 \sin ω t : y = 2 \sin (ω t + \frac{π}{4})$
The path of the particle will be
(a) a straight line (b) a circle (c) an ellipse (d) a parabola