Question

The equation of a particle executing simple harmonic motion is given by x = sin π `("t" + 1/3)` m. At t = 1s, the speed of particle will be ______. (Given π = 3.14)

Options

• 0 cm s^-1

• 157 cm s^-1

• 272 cm s^-1

• 314 cm s^-1

Answer 1

The equation of a particle executing simple harmonic motion is given by x = sin π `("t" + 1/3)` m. At t = 1s, the speed of particle will be 157 cm s^-1. (Given π = 3.14)

Explanation:

At t = 1 sec

x = sin π `("1" + 1/3)` 

= sin`(4pi)/3`

= `-sqrt3/2`

So, V = ω`sqrt("A"^2-x^2)`

= π `sqrt(1-3/4)`

= `pi/2` m/s

= 157 cm/s