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?

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 = 1.25 m/s

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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