The maximum velocity and the maximum acceleration of a body executing simple harmonic oscillator are 2 m/s and 4 m/s2 and Then angular velocity will be A. 3 rad/sec B. 0.5 rad/sec C. 1 rad/sec D. 2 rad/sec

The correct option is (D)

The maximum acceleration of a body executing simple harmonic motion of amplitude A and angular velocity ω is given by

a_max = ω²A

The maximum velocity of a body executing simple harmonic motion of amplitude A and angular velocity ω is given by

v_max = ωA

Taking the ratio of maximum acceleration to maximum velocity, we get

\(\frac{a_{max}}{v_{max}} = \frac{\omega^2A}{\omega A} = \omega\)

Hence, the angular velocity of the body is the ratio of maximum acceleration to maximum velocity

⇒ ω = \(\frac{a_{max}}{v_{max}}\)

Given in question,

Maximum acceleration of the body, a_max = 4 m/s²

Maximum velocity of the body, v_max = 2 m/s

Therefore, the angular velocity of the body is given by

ω = \(\frac{a_{max}}{v_{max}}\) = \(\frac{4}{2}\) = 2 rad/sec

---

Also Read: