Question

Time period of simple harmonic oscillator is T. In what time will it traverse a distance equal to half of amplitude from mean position?

Solution

The displacement of particle executing simple harmonic oscillation is given by,
y = A sin ωt

Let the particle take t_o time to go from mean position to half of extreme position.
Therefore,
$therefore space space space space space space space space space straight A over 2 equals straight A space s i n space omega t subscript 0 rightwards double arrow space space space space space space space space space space s i n space omega t subscript 0 equals 1 half rightwards double arrow space space space space space space space space space space space omega t subscript straight omicron equals straight pi over 6 rightwards double arrow space space space space space space space space space straight t subscript 0 equals fraction numerator straight pi over denominator 6 straight omega end fraction equals fraction numerator straight pi cross times straight T over denominator 6 cross times 2 straight pi end fraction equals straight T over 12$
So, at a time of $straight T over 12$ the simple harmonic oscillator is equal to half of amplitude from the mean position.

Some More Questions From Mechanical Properties of Fluids Chapter

For Daily Free Study Material Join wiredfaculty

Mechanical Properties Of Fluids

Time period of simple harmonic oscillator is T. In what time will it traverse a distance equal to half of amplitude from mean position?

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

Phone Number

Email Address

Location