Question

in fig. 15.12, two identical springs of spring constant 7580 n/m are attached to a block of mass 0.245 kg. what is the frequency of oscillation on the frictionless floor?

Answer 1

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 = $\sqrt{2k/m}$

w = $\sqrt{2*7580/0.245}$

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

Learn more about Frequency here, brainly.com/question/14320803

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