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Question

The displacement of a harmonic oscillator is given by x=asinωt+βcosωt. The amplitude of the oscillator is

A
a
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B
β
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C
a+β
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D
a2+β2
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Solution

The correct option is D a2+β2
x=asinωt+βcosωt
or, x=a2+b2(aa2+b2sinωt+βa2+b2cosωt)

Thus, x=a2+b2(sin(ωt+θ)) (using the property, sin(x+y)=sin x cos y + sin y cos x)

Thus it's of form x=Asinωt, where A=a2+b2

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