Critical damping resistance measurement using ballastic galvanometer For multiple aperture size laser beam projector Abstract A ballistic galvanometer will oscillate if it has not been properly damped. Galvanometers are damped by adding a shunt resistor of just the right amount of resistance in parallel with them. The proper amount of resistance at which the motion just ceases to be oscillatory is called the critical external damping resistance (CXDR). When shunted by its CXDR, the galvanometer is said to be critically damped. With more resistance it is underdamped and with less it is overdamped. When the galvanometer is critically damped, it will make one swing and return slowly to its zero position. Critical Damping We can use these equations to discover when the energy dies out smoothly (over-damped) or rings (under-damped). Look at the term under the square root sign, which can be simplified to: R 2 C 2 -4LC When R 2 C 2 -4LC is positive, then α and β are real numbers and the oscillator is over-damped. The circuit does not show oscillation. When R 2 C 2 -4LC is negative, then α and β are imaginary numbers and the oscillations are under-damped. The circuit responds with a sine wave in an exponential decay envelope.
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Critical damping resistance measurement using ballastic galvanometer
For multiple aperture size laser beam projector
Abstract
A ballistic galvanometer will oscillate if it has not been properly damped. Galvanometers are damped by adding a
shunt resistor of just the right amount of resistance in parallel with them. The proper amount of resistance at which
the motion just ceases to be oscillatory is called the critical external damping resistance (CXDR). When shunted by
its CXDR, the galvanometer is said to be critically damped. With more resistance it is underdamped and with less
it is overdamped. When the galvanometer is critically damped, it will make one swing and return slowly to its zero
position.
Critical Damping
We can use these equations to discover when the energy dies out smoothly (over-damped) or rings (under-damped).
Look at the term under the square root sign, which can be simplified to: R2C2-4LC
When R2C2-4LC is positive, then α and β are
real numbers and the oscillator is over-damped.
The circuit does not show oscillation.
When R2C2-4LC is negative, then α and β are
imaginary numbers and the oscillations are
under-damped. The circuit responds with a sine
wave in an exponential decay envelope.
When R2C2-4LC is zero, then α and β are zero
and oscillations are critically damped. The
circuit response shows a narrow peak followed
by an exponential decay.
Purpose of the experiment:
Data table :
Observation no Resistance Ω Deflection Cm cdrΩ error
To observe damped oscillations in the RLC ci
rcuit and measure the amplitude, period, angular
frequency, damping constant and log decrement
of damped oscillatory signals. To find the
critical resistance for which the critical damping occurs.
2. What to learn?
Transfer of energy in LC circuit. The elec
trical-mechanical analogy. Differential equation
describing damped simple harmonic motion in
the RLC circuit.. Solution of this equation.
Angular frequency of the damped oscillator.
Damping constant. Angular frequency of the
undamped oscillator. Forced oscillations and re
sonance. Kirchhoff's rules. Log decrement of
damped oscillatory signals. Critical da
mping. How does the oscilloscope work?
Logarithmic decrement: The logarithmic decrement is defined a the ratio of any two successive peak amplitudes
natural logarithm as we can see in the damped simple harmonic motion if aA and A ‘ are two amplitude then
logarithmic decrement is log a/a’
The logarithmic decrement represents the rate at which the amplitude of a free damped vibration decreases. It is