1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# A particle undergoes mutually perpendicular simple harmonic motions given by x=acosωt and y=asinωt. The trajectory of motion of the particle will be

A
an ellipse
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
a parabola
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
a circle
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
a straight line
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C a circle Given the SHM equations in x and y directions are x=acosωt ........(i) y=asinωt ........(ii) Squaring and adding equations (i) and (ii), we get x2+y2=a2(cos2ωt+sin2ωt) ⇒x2+y2=a2 [∵cos2ωt+sin2ωt=1] This is the equation of a circle of radius a with centre at the origin. Hence, the trajectory of motion of the particle will be a circle.

Suggest Corrections
1
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program