Two bodies P and Q of equal asses are suspended from two separate springs of constants K₁ and k₂ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, then what is the ratio of the amplitudes of vibration of P and Q?

Solution

Frequency of oscillation of body P is,

straight omega subscript 1 equals square root of straight K subscript 1 over straight m end root

Frequency of oscillation of body Q is,

straight omega subscript 1 over straight w subscript 2 equals square root of straight K subscript 2 over m end root

The ratio of the frequency of oscillation of body P to Q is,

straight omega subscript 1 over straight omega subscript 2 equals square root of straight K subscript 1 over straight K subscript 2 end root

Let, A₁and A₂be the amplitude of oscillation of P and Q respectively.
Since the velocity of P and Q at mean position (maximum velocity) is equal, therefore

space space space space space space space space space straight A subscript 1 straight omega subscript 1 equals straight A subscript 2 straight omega subscript 2 space rightwards double arrow space space space space straight A subscript 1 over straight A subscript 2 equals straight omega subscript 2 over straight omega subscript 1 equals square root of straight K subscript 2 over straight K subscript 1 end root

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

Two bodies P and Q of equal asses are suspended from two separate springs of constants K₁ and k₂ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, then what is the ratio of the amplitudes of vibration of P and Q?

Some More Questions From Mechanical Properties of Fluids Chapter

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.

What is the net displacement of the particle executing simple harmonic motion in one complete oscillation?

Are all the periodic motions simple harmonic?

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Mechanical Properties Of Fluids

Two bodies P and Q of equal asses are suspended from two separate springs of constants K1 and k2 respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, then what is the ratio of the amplitudes of vibration of P and Q?

Some More Questions From Mechanical Properties of Fluids Chapter

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.

What is the net displacement of the particle executing simple harmonic motion in one complete oscillation?

Are all the periodic motions simple harmonic?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Two bodies P and Q of equal asses are suspended from two separate springs of constants K₁ and k₂ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, then what is the ratio of the amplitudes of vibration of P and Q?