Mechanical Properties of Fluids

Question

A spring oscillates with frequency 30 per minute when loaded by M kg. On increasing the load by 0.5 kg, the frequency of oscillation decreases to 24 per minute. Find M.

Solution

The frequency of oscillation is given by,
$straight nu space equals space fraction numerator 1 over denominator 2 straight pi end fraction square root of straight k over straight m end root$
Given, when m = M ; $straight nu space equals space 30 space per space min$
$therefore space 30 space equals space fraction numerator 1 over denominator 2 straight pi end fraction square root of straight k over straight m end root space space space space space space space space space space space space space... space left parenthesis 1 right parenthesis thin space When comma space straight m space equals space straight M space plus space 0.5 comma space then space space space space space space space space space space space space space space straight nu space equals space 24 space per space min So comma space space 24 space equals space fraction numerator 1 over denominator 2 straight pi end fraction space square root of fraction numerator straight k over denominator straight M plus 0.5 end fraction end root space space space space space space... space left parenthesis 2 right parenthesis thin space Dividing space equation space left parenthesis 1 right parenthesis space by space left parenthesis 2 right parenthesis comma space we space get space space space space space space space 30 over 24 space equals space square root of fraction numerator straight M space plus space 0.5 over denominator straight M end fraction end root space rightwards double arrow space space fraction numerator straight M space plus space 0.5 over denominator straight M end fraction space equals space 25 over 16 rightwards double arrow space space space 16 space straight M space plus space 8 space equals space 25 space straight M space rightwards double arrow space space space space 9 space straight M space equals space 8 space rightwards double arrow space space space space space space straight M space equals space 8 over 9 kg$

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Mechanical Properties Of Fluids

A spring oscillates with frequency 30 per minute when loaded by M kg. On increasing the load by 0.5 kg, the frequency of oscillation decreases to 24 per minute. Find M.

Some More Questions From Mechanical Properties of Fluids Chapter

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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