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 8.0 cm and a period of 0.80 s.
Part A: What is the wingtips' maximum speed?
Part B: What is the wingtips' maximum acceleration?

Answer 1

Answer:

PART A: Maximum speed = 0.314 m/s

PART B: Maximum acceleration = 1.23 m/s²

Explanation:

A simple Harmonic motion is a repetitive motion through an equilibrium point.

Amplitude = 8.0cm = 8/100 = 0.08m (highest displacement)

period (T) = 0.80s

A) maximum speed $(V_{max)$

$V_{max} = 2\pi fA\\where:\\A = Amplitude = 0.08m\\f = frequency = \frac{1}{period(T)} = \frac{1}{0.8} = 1.25 Hz\\\therefore 2\pi fA = 2\pi \times 1.25 \times 0.08\\= 0.314\ m/s$

B) maximum acceleration $(a_{max})$

$a_{max} = (2\pi f)^2A\\where:\\f = 1.25Hz\\A = 0.08m\\a_{max} = (2\pi \times 1.25)^2 \times 0.08\\= 1.23\ m/s^2$