The frequency of oscillation on the frictionless floor is 39.6Hz
Frequency is defined as the number of oscillations in unit time.
The net force applied by the springs to bring the block back to equilibrium when it is out of balance is -2kx acting in that direction.
We know that,
a = dx²/dt²
From Newton second law of motion,
F = ma
mdx²/dt² = -2kx
On substituting, x=x' cos(ωt+ϕ) where x' is the position at mean position.
We get, w² = 2k/m
Hence, w = [tex]\sqrt{2k/m}[/tex]
w = [tex]\sqrt{2*7580/0.245}[/tex]
w = 248.75
Since there are 2π radians in a cycle, and frequency f measures cycles per second,
f = w/2π
On substituting the value of w,
f = 248.75/2π
f = 39.6Hz
Hence, the frequency of oscillation on the frictionless floor is 39.6Hz
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