Question

Two simple harmonic motion are represented by the equation X1=4sin2pit and x2=2[sin2pit+cos2pit].What is the ratio of their amplitude.

Answer 1

Answer:

Ratio of the amplitude of two given SHM is 1.414 : 1

Explanation:

As we know that we have two SHM equations given here

so for the first SHM we have

$x_1 = 4 sin 2\pi t$

so amplitude of the above motion is

$A_1 = 4$

for another SHM we have

$x_2 = 2(sin2\pi t + cos2\pi t)$

so we can write it is

$x_2 = 2\sqrt2 sin(2\pi t + \frac{\pi}{4})$

so the amplitude of this motion is

$A_2 = 2\sqrt2$

now the ratio of the amplitude of the two motion is given as

$A_1 : A_2 = 4 : 2\sqrt 2$

$A_1 : A_2 = 1.414 : 1$

#Learn

Topic : SHM

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