The image above represents velocity.

To compute for velocity, three essential parameters are needed and these parameters are **angular velocity (ω), amplitude (A) **and **displacement (y).**

The formula for calculating velocity:

v = ω√(A² – y²)

Where;

v = Velocity

ω = Angular Velocity

A = Amplitude

y = Displacement

Let’s solve an example;

Find the velocity when the angular velocity is 7, amplitude is 10 and displacement is 13.

This implies that;

ω = Angular Velocity = 7

A = Amplitude = 10

y = Displacement = 13

v = ω√(A² – y²)

v = 7 x √(10² – 13²)

v = 7 x √(100 – 169)

v = 7 x √(-69)

i signifies a complex number = √(-1).

v = 7 x √(69) x √(-1)

v = 7 x √(69)i

v = 7 x 8.30i

v = 7(8.30i)

Therefore, the **velocity **is **7(8.30i) m/s.**

**Calculating the Angular Velocity when the Velocity, the Amplitude and the Displacement is Given.**

ω = ^{v} / _{√(A2 – y2)}

Where;

ω = Angular Velocity

v = Velocity

A = Amplitude

y = Displacement

Let’s solve an example;

Find the angular velocity when the velocity is 28, the amplitude is 14 and the displacement is 10.

This implies that;

v = Velocity = 28

A = Amplitude = 14

y = Displacement = 10

ω = ^{v} / _{√(A2 – y2)}

ω = ^{28} / _{√(142 – 102)}

ω = ^{28} / _{√(196 – 100)}

ω = ^{28} / _{√(96)}

ω = ^{28} / _{9.79}

ω = 2.86

Therefore, the **angular velocity **is **2.86.**

Continue reading How to Calculate and Solve for Velocity | Motion