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Damped Harmonic motion is considered one the most difficult concept.
14 Questions around this concept.
A pendulum with time period of 1s is losing energy due to damping. At certain time its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, its damping constant (in s-1) is :
The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds.Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to
The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will decrease to times its original magnitude, where
equals :
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Free\undamped oscillation-
Damped oscillation-
where
u=velocity
= damping force
b= damping constant
= restoring force
Or using
where x=displacement of damped oscillation
we can write, The equation of motion of Damped oscillation as
The solution of the above differential equation will give us the formula of x as
where
and
where
Critical damping happens at
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