Question

We can model the motion of a dragonfly's wing as simple harmonic motion. The total distance between the upper and lower limits of motion of the wing tip is 1.0 cm. The wing oscillates at 40 Hz. What is the maximum speed of the wing tip?

Answer 1

Answer:

The maximum speed of the wing tip is 1.25 m/s

Explanation:

In simple harmonic motion, the body experiences a restoring force whose magnitude is directly proportional to the distance from its mean position and its direction is towards the mean position.

The speed in the case of simple harmonic motion is given by the equation :

v = Aωsinωt

Here A is maximum displacement, t is time and ω is the angular frequency of oscillation.

For maximum speed, sinωt = 1 . So, the above equation becomes:

v = Aω

But, ω = 2πf , here f is the frequency of oscillation. So,

v = A x 2πf      .....(1)

In this problem,

Frequency of oscillation, f = 40 Hz

Total distance between the upper and lower limits of motion of wing tip is equal to the twice of maximum displacement of the wing tip from the equilibrium position, i.e. ,

2 x A = 1 cm

A = 0.5 cm = 0.5 x 10⁻² m

Substitute the value of f and A in equation (1).

$v=2\pi\times40\times0.5\times10^{-2}$

v = 1.25 m/s