Question

An object undergoing simple harmonic motion has amplitude of 2.3 m. if the maximum velocity of the object is 15 m/s, what is the object's angular frequency?

Answer 1

Answer:

Angular frequency, $\omega=6.52\ rad/s$

Explanation:

Given that,

Amplitude of simple harmonic motion, A = 2.3 m

Maximum velocity of the object, $v_{max}=15\ m/s$

To find,

The object's angular frequency.

Solution,

The equation of the displacement of particle is given by :

$y=A\ cos(\omega t)$

On differentiating above equation, we get the expression for maximum velocity as :

$v_{max}=A\times \omega$

$\omega=\dfrac{v_{max}}{A}$

$\omega=\dfrac{15\ m/s}{2.3\ m}$

$\omega=6.52\ rad/s$

So, the angular frequency of the object is 6.52 rad/s.

Answer 2

Using:
v = Aωcos(ωt), at t = 0, A = 2.3 m and v = 15 m/s
ω = 15/2.3
ω = 6.52 rad/s