Question

Vision is blurred if the head is vibrated at 29 Hz because the vibrations are resonant with the natural frequency of the eyeball in its socket. If the mass of the eyeball is 7.5 g, a typical value, what is the effective spring constant of the musculature that holds the eyeball in the socket?

Answer 1

k = 4422.35 KN/m

Step-by-step explanation:

Given that

Frequency ,f= 29 Hz

m = 7.5 g

Natural frequency ω

ω = 2 π f

We also know that for spring mass system

ω ² m =k

k=Spring constant

So we can say that

( 2 π f)² = m k

By putting the values

(2 x π x 29)² = 7.5 x 10⁻³ k

33167.69 = 7.5 x 10⁻³ k

k=4422.35 x 10³ N/m

k = 4422.35 KN/m

Therefore spring constant will be 4422.35 KN/m