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Two mutually perpendicular simple harmon...

Two mutually perpendicular simple harmonic vibrations have same amplitude, frequency and phase. When they superimpose, the resultant form of vibration will be

A

a circle

B

a straight line

C

a parabola

D

an ellipse

Text Solution

Verified by Experts

The correct Answer is:
B
Two mutually perpendicular simple harmonic vibrations are combined. Let the equations be

`x = a sin omega t` and `y = a sin omega t`
`x^(2) + y^(2) = 2a^(2) sin^(2) omega t = 2 xx a sin omega t xx a sin omega t`
`x^(2) + y^(2) = 2xy`
`(x-y)^(2) = 0` or y = x
This equations represents a straight line.
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