Question

Two particles are executing simple harmonic motion of the same amplitude Aand frequency ω along the x - axis. Their mean position is separated by distance X₀ (X₀ >A). If the maximum separation between them is (X0 + A), the phase difference between their motion is

π/3

π/4

π/6

π/2

Solution

π/3

x₁ = A sin( ωt + Φ₁)
x₂ = A sin( ωt + Φ₂)
$straight x subscript 1 space minus straight x subscript 2 space equals space straight A space open square brackets 2 sin open square brackets ωt space plus space fraction numerator straight ϕ subscript 1 plus straight ϕ subscript 2 over denominator 2 end fraction close square brackets sin open square brackets fraction numerator straight ϕ subscript 1 minus straight ϕ subscript 2 over denominator 2 end fraction close square brackets close square brackets straight A space equals space 2 straight A space sin space open parentheses fraction numerator straight ϕ subscript 1 minus straight ϕ subscript 2 over denominator 2 end fraction close parentheses fraction numerator straight ϕ subscript 1 minus straight ϕ subscript 2 over denominator 2 end fraction space equals space straight pi over 6 straight ϕ subscript 1 space equals space straight pi over 3$

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

Two particles are executing simple harmonic motion of the same amplitude Aand frequency ω along the x - axis. Their mean position is separated by distance X₀ (X₀ >A). If the maximum separation between them is (X0 + A), the phase difference between their motion is

π/3

π/4

π/6

π/2

Some More Questions From Mechanical Properties of Fluids Chapter

Define frequency.

What is the condition for motion to be simple harmonic motion?

In the displacement equation y = r sin(ωt/ + ϕ) what does ϕ called and what information does it give?

What determines the natural frequency of an oscillator?

Is there any relation between uniform circular motion and simple harmonic motion?

What is periodic motion?

Write down the expression for the instantaneous velocity and acceleration of particle vibrating in simple harmonic motion.

How do you define the mean position of particle executing simple harmonic motion?

Define amplitude.

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For Daily Free Study Material Join wiredfaculty

Mechanical Properties Of Fluids

Two particles are executing simple harmonic motion of the same amplitude Aand frequency ω along the x - axis. Their mean position is separated by distance X0 (X0 >A). If the maximum separation between them is (X0 + A), the phase difference between their motion is π/3 π/4 π/6 π/2

Some More Questions From Mechanical Properties of Fluids Chapter

Define frequency.

What is the condition for motion to be simple harmonic motion?

In the displacement equation y = r sin(ωt/ + ϕ) what does ϕ called and what information does it give?

What determines the natural frequency of an oscillator?

Is there any relation between uniform circular motion and simple harmonic motion?

What is periodic motion?

Write down the expression for the instantaneous velocity and acceleration of particle vibrating in simple harmonic motion.

How do you define the mean position of particle executing simple harmonic motion?

Define amplitude.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Two particles are executing simple harmonic motion of the same amplitude Aand frequency ω along the x - axis. Their mean position is separated by distance X₀ (X₀ >A). If the maximum separation between them is (X0 + A), the phase difference between their motion is

π/3

π/4

π/6

π/2