A simple harmonic oscillator has an amplitude \alpha and time period T. The time required by it to travel from x = \alpha  to  x = \frac{\alpha}{2}  is

  • Option 1)

    4.0\: s

  • Option 2)

    2.0\: s

  • Option 3)

    1.0\: s

  • Option 4)

    0.5\: s

 

Answers (1)
A Avinash

It is required to calculate the time from extreme position. Hence, in this case equation for displacement of particle can be written as \\*x = a\sin(\omega t + \frac{\pi}{2}) = a\cos\omega t \\*\Rightarrow \frac{a}{2} = a\cos \omega t \Rightarrow \omega t = \frac{\pi}{3} \Rightarrow \frac{2\pi}{T}\cdot t = \frac{\pi}{3} \Rightarrow t = \frac{T}{6}

 

Time Period -

Since all periodic motion repeat themselves in equal time interval. This minimum time interval is known as time period for oscillation.

- wherein

It is denoted by T.

 

 

 


Option 1)

4.0\: s

This is correct.

Option 2)

2.0\: s

This is incorrect.

Option 3)

1.0\: s

This is incorrect.

Option 4)

0.5\: s

This is incorrect.

Exams
Articles
Questions