Question

A mass M, attached to a horizontal spring, executes SHM with an amplitude A₁. When the mass M passes through its mean position than a smaller mass m is placed over it and both of them move together with amplitude A₂. The ratio of (A₁/A₂) is

$fraction numerator straight M space plus straight m over denominator straight M end fraction$
$open parentheses fraction numerator straight M over denominator straight M plus straight m end fraction close parentheses to the power of 1 divided by 2 end exponent$

$fraction numerator straight M over denominator straight M plus straight m end fraction$

Solution

At mean position, F_net = 0
Therefore, By conservation of linear momentum,
Mv₁ = (M+m)v₂
Mω₁A₁ = (M+m)ω₂A₂
⇒ $rightwards double arrow space open parentheses fraction numerator straight M over denominator straight M plus straight m end fraction close parentheses space equals space fraction numerator straight omega subscript 2 straight A subscript 2 over denominator straight omega subscript 1 straight A subscript 1 end fraction But space straight omega subscript 1 space equals space square root of straight k over straight M end root space and space straight omega subscript 2 space equals space square root of fraction numerator straight k over denominator straight M plus straight m end fraction end root On space solving comma space we space get space straight A subscript 1 over straight A subscript 2 space equals space square root of fraction numerator straight m plus straight M over denominator straight M end fraction end root$

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

Some More Questions From Mechanical Properties of Fluids Chapter

What is temperature coefficient?

What is periodic motion?

What is an oscillatory motion?

What is time period?

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?

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Mechanical Properties Of Fluids

A mass M, attached to a horizontal spring, executes SHM with an amplitude A1. When the mass M passes through its mean position than a smaller mass m is placed over it and both of them move together with amplitude A2. The ratio of (A1/A2) is

Some More Questions From Mechanical Properties of Fluids Chapter

What is temperature coefficient?

What is periodic motion?

What is an oscillatory motion?

What is time period?

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?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation