Question

A body oscillates simple harmonically according to equation y=5 cos( $3 pi t plus pi over 3 right parenthesis c m$ What is displacement, velocity and acceleration at t= 3s?

Solution

Simple Harmonic Equation is given by,
y = 5cos(3 $pi t plus pi over 3 right parenthesis c m$
Therefore,
Velocity, v $equals space dy over dt space equals space minus 15 space straight pi space left parenthesis 3 πt space plus space straight pi over 3 right parenthesis space cm space divided by straight s$
$Acceleration comma space straight a space equals space dv over dt space equals space minus 45 space straight pi squared space cos space open parentheses 3 πt space plus space begin inline style straight pi over 3 end style close parentheses space cm divided by straight s squared$
Now, y (t=3) = 5 cos (9 $straight pi space plus space straight pi over 3 right parenthesis thin space cm$
= $negative 5 space cos space open parentheses straight pi over 3 close parentheses space cm space equals space minus 2.5 space space cm space$
Therefore,
v|_t=3= -15 $straight pi space sin space open parentheses begin inline style straight pi over 3 end style close parentheses space cm divided by sec space equals space fraction numerator 15 straight pi square root of 3 over denominator 2 end fraction space cm divided by sec$
Acceleration, a|_t=3 = $negative 45 space straight pi squared space cos space left parenthesis 9 straight pi space plus space straight pi over 3 right parenthesis space cm divided by straight s squared$
$equals space 45 space straight pi squared space cos space open parentheses straight pi over 3 close parentheses space cm divided by straight s squared$
= $fraction numerator 45 space straight pi squared over denominator 2 end fraction space c m divided by s squared$

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

A body oscillates simple harmonically according to equation y=5 cos( $3 pi t plus pi over 3 right parenthesis c m$ What is displacement, velocity and acceleration at t= 3s?

Some More Questions From Mechanical Properties of Fluids Chapter

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?

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

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For Daily Free Study Material Join wiredfaculty

Mechanical Properties Of Fluids

A body oscillates simple harmonically according to equation y=5 cos( What is displacement, velocity and acceleration at t= 3s?

Some More Questions From Mechanical Properties of Fluids Chapter

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?

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

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A body oscillates simple harmonically according to equation y=5 cos( $3 pi t plus pi over 3 right parenthesis c m$ What is displacement, velocity and acceleration at t= 3s?