Question

16 TWO SHMs with same amplitude and time period.
when acting together in perpendicular directions
with a phase difference of
$\pi \div 2$

give rise to
(1) Straight motion
(2) Elliptical motion
(3) Circular motion
(4) None of these​

Answer 1

Answer:

(3) circular motion

Explanation:

Eqn of circle is a^2= x^2 + y^2

plz refer the above soln

Answer 2

Two SHMs with same amplitude and time period when acting together in perpendicular directions  with a phase difference of  π / 2 gives rise to "Circular motion".

Option (3) is correct.

Explanation:

Two SHMs with same amplitude and time period when acting together in perpendicular directions  with a phase difference of  π / 2 gives rise to "Circular motion".

x = a sinωt

y = a sin ( ωt + π / 2 ) = a cos ωt

x / y = sin ωt / cos ωt = tan ωt

x / y = x / √ a^2 - x^2

y^2 = a^2 - x^2

This is an equation of circle.