the mass of the system must be quadrupled
here,
the initial spring constant is K0
the final spring constant , K = 4 * K0
when the frequency remains the same
(1/2*pi) * sqrt(K/m) = (1/2*pi) * sqrt(K0/m0)
K/m = K0 /m0
4 * K0 /m = K0 /m0
m = 4 * m0
the mass of the system must be quadrupled
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x:
where k is a positive constant. If the only force acting on a
system is F, the system is called a simple harmonic oscillator, and it oscillates simply. Sinusoidal oscillation of constant amplitude and constant frequency (independent of amplitude) around the equilibrium point.
A harmonic oscillator is called a damped oscillator if there is also a frictional force (damping) proportional to velocity. Depending on the coefficient of friction, the system can:
Oscillates at a lower frequency than undamped and decreases in amplitude over time (underdamped oscillator). The
damps to its equilibrium position without oscillation (overdamped oscillator).
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