Physics
Grade-9
Easy

Question

The periodic time of a body executing simple harmonic motion is 3 sec. After how many intervals from time t = 0, its displacement will be half of its amplitude:

  1.  1 over 6sec
  2.  1 fourthsec
  3. 1 thirdsec
  4. 1 over 8sec

hintHint:

The equation for SHM is given by,

y=Asinωt and ω=2πf=2π/T

The correct answer is: 1 fourthsec


    Given that, time period T=3seconds.

    The equation for SHM is given by, 

    y=Asinωt and ω=2πf=2π/T

    Let after time t=t, the displacement is half its amplitude, 

    A​/2=Asin(2πt/3)

    sin(π/6)=sin(2πt/3)
    or, t=1​/4 sec is our required answer.

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