Question

If x = `5 sin (pi t + pi/3) m` represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are ______.

विकल्प

• 5 cm, 1 s

• 5 m, 1 s

• 5 cm, 2 s

• 5 m, 2 s

Answer 1

If x = `5 sin (pi t + pi/3) m` represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are 5 m, 2 s.

Explanation:

The given equation is:

x = `5 sin (pi t + pi/3) m`

Comparing the above equation with x = A sin (ωt + Φ), we get,

A = 5 m

The angular frequency ω is the coefficient of t in the equation:

ω = π rad s⁻¹

The relationship between the time period (T) and angular frequency (ω) is given by:

T = `(2 pi)/omega`

Substituting ω = π:

T = `(2 pi)/omega`

= 2 s