Question

The motion of a nightingale's wingtips can be modeled as simple harmonic motion. In one study, the tips of a bird's wings were found to move up and down with an amplitude of 8.6 cm and a period of 0.80 s.

A) What is the wingtips' maximum speed?

B) What is the wingtips' maximum acceleration?

Answer 1

Amplitude of the motion = A = 8.6 cm = 0.086 m

Time period = T = 0.8 sec

Angular frequency =

= 7.854 rad/s

Maximum speed = V

In a simple harmonic motion maximum speed is given by,

V = A

V = (0.086)(7.854)

V = 0.675 m/s

Maximum acceleration = a

In a simple harmonic motion maximum acceleration is given by,

a = A²

a = (0.086)(7.854)²

a = 5.305 m/s²

A) Wingtip's maximum speed = 0.675 m/s

B) Wingtip's maximum acceleration = 5.305 m/s²