Question

Obtain an equation for the frequency of oscillation of spring of force constant k to which a mass m is attached.

Answer 1

suppose extension in spring is x so restoring force acting on mass will be
F = -Kx
We know force on a Body is
F = ma
Where m is the mass of particle and a is the acceleration of the particle, so acceleration of the body can be written as
a = F/m
so acceleration of mass is
a = -Kx/m
or a = -(K/m)x

condition of simple harmonic motion, a =- $\omega^2x$

so, $\omega^2=\frac{K}{m}$

$\omega=\sqrt{\frac{k}{m}}$

we know, $\omega=2\pi\eta$
where $\eta$ indicates frequency.

so, $\boxed{\eta=\frac{1}{2\pi}\sqrt{\frac{k}{m}}}$

Answer 2

Answer:

frequency=1/2π √k/m

Explanation:

y=w square x