Question

A small fly of mass 0.25 g is caught in a spider's web. The web vibrates predominately with a frequency of 4.6 Hz .What is the value of the effective spring stiffness constant k for the web?At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?

Answer 1

Into the equation for shm, a = (-)ω²x .. .. sub a = F/m
F/m = ω² x
F/x = k = ω² m .. .. sub ω = 2πf ..

k = (2πf)² m = (2π 4.60)² *0.25^-3(kg) .. .. ►k = 0.53 N/m

(b) k = (2πf)² m .. (see above)
0.23 = 4π² f² *0.48^-3(kg)

f² = 0.23 / (4π² *0.50^-3) = 12.10 .. .. f = √12.10 .. .. ►f = 2.60 Hz