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

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

Step-by-step 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* \omega`

`\omega=(v_(max))/(A)`

`\omega=(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