Question

The motion of a particle is given by x = Asinωt + Bcosωt.

Answer 1

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simple harmonic with amplitude A + B

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Answer 2

Answer:

The motion of the particle is Circular.

Explanation:

x = asinωt

$\frac{x}{a}$ = sinωt    .. (1)

y = acosωt

$\frac{y}{a}$ = cosωt    .. (2)

Squaring and adding both the equations:

we get,

$\frac{x^{2} }{a^{2} } + \frac{y^{2} }{a^{2} } = 1$     ..(∵ $cos^{2}$ ωt + $sin^{2}$ ωt = 1)

$x^{2} + y^{2} = a^{2}$

This is the equation of a circle.

∴ Particle follows a circular path.

∴ The motion of the particle is Circular.