Question

The amplitude of the motion u = 4cos 3t - 2 sin 3t is
a) √5
b) 3√5
c) 5√5
d) 2√5​

Answer 1

Answer:

Option (b)

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Answer 2

The amplitude of the motion is $2\sqrt5$ .

Given :

Displacement of a particle at time t is :

$u=4cos\ 3t-2sin\ 3t$

We need to find the amplitude of its motion .

We know , amplitude is the peak ( maximum ) value of a function .

Also , maximum value of mathematical function :

$y=asin\ x+bcos\ x$ form is given by :

$y_{max}=\sqrt{a^2+b^2}$

Comparing it with given equation :

We get , amplitude as :

$A=\sqrt{4^2+2^2}\\A=2\sqrt5$

Therefore , the amplitude of the motion is $2\sqrt5$ .

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Kinematics

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