help@askiitians.com

1800-150-456-789

Most Scoring Topics in IIT JEE> A simple harmonic oscillator has an ampli...

question mark

A simple harmonic oscillator has an amplitude A and time period T the time required by it to travel from x=A to x=A/2 is?

Zain , 6 Years ago

Grade 12th pass

3 Answers

Eshan

Last Activity: 6 Years ago

Dear student,

Since the particle starts from x=A, the equation of motion can be written as

$x=Acos\omega t$
Hence for $x=A/2$ ,
$A/2=Acos\omega t\implies \omega t=\dfrac{\pi}{3}$
$\implies t=\dfrac{\pi}{3\omega}$
Since $T=\dfrac{2\pi}{\omega}$ ,
$t=T/6$

Dev Kumar

Last Activity: 6 Years ago

You could've been answered the question with the help of concept of phaser diagram.

In this, draw a circle of radius A on a Cartesian sheet, and on y-axis mark a point A/2 on +y-axis,and at the end point of circle mark point A

Particle shm => A----->A/2 ; can be considered as A/2---->A

Draw a line from A/2 projecting on the circle, join the origin and projection, take angle along y-axis and mark it as μ.

Now cos μ= A/2A= 1/2 => μ=π/3

We know that,

μ/t= 2π/T

=> π/3t=2π/T

=> t= T/6

Kushagra Madhukar

Last Activity: 4 Years ago

Dear student,

Please find the attached solution to your problem.

Assume x = 0 as t = 0 and T be the period of SHM

Time taken to travel between extreme position, x = A and initial position, x = 0 is T/4

Now, x = A sin(2π/T * t)

A/2 = A sin(2π/T * t)

or, t = T/12

Hence, time taken to reach x = A/2 from x = A is

T/4 – T/12 = T/6

Hope it helps

Thanks and regards,

Kushagra

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

scoring chapters from inter 1^st year in iit to get atleast below 2000 raks

most scoring topics in iit jee

2 Answers Available

Last Activity: 4 Years ago

iam a very average student...and i want to crack jee mains 2021...in this last 7days figure me out on which easy topics i should focus for better score

most scoring topics in iit jee

2 Answers Available

Last Activity: 4 Years ago

Two parallel beams of light P and Q are incident normally on a prism and the transmitted rays are brought to focus with the help of a convergent lens as shown. If the intensities of the upper and lower beams immediately after transmission from face AC are 4I abd I, respectively, find the resultant intensity at the focus.

most scoring topics in iit jee

1 Answer Available

Last Activity: 4 Years ago

Tell me the most scoring chapters in maths and chemistry..... And some hacks to solve mcq also...

most scoring topics in iit jee

0 Answer Available

Last Activity: 4 Years ago

The system of connected flexible cables shown in the figure is supporting 2 loads of 550N and 600N at points B and D. Determine the tensions in various segments of the cable

most scoring topics in iit jee

1 Answer Available

Last Activity: 4 Years ago

View all Questions