Which condition is suitable for indicating instruments in order to get the best results?
Damped slightly less than the critical value
Understanding Damping in Indicating Instruments
Indicating instruments, like ammeters and voltmeters, use a pointer that moves over a scale to show the value of the quantity being measured. When the quantity changes, the pointer moves. To get an accurate reading, the pointer needs to settle quickly at the final value without oscillating excessively.
This is where damping comes in. Damping is a force that opposes the motion of the pointer and brings it to rest. Different levels of damping result in different pointer behaviors:
- Under Damped: If the damping is too low, the pointer will oscillate back and forth around the final reading before eventually settling. This makes it difficult to read the instrument accurately and quickly.
- Critically Damped: This is the theoretical condition where the pointer moves to the final reading as quickly as possible without any oscillation or overshoot. It settles directly at the steady-state position.
- Over Damped: If the damping is too high, the pointer will move slowly towards the final reading. There is no oscillation, but the pointer takes a long time to reach the steady-state position.
Optimal Damping for Best Results
For indicating instruments, we want the pointer to settle quickly so that readings can be taken promptly. While critical damping offers the fastest settlement without overshoot, in practice, achieving perfect critical damping is difficult.
Often, a condition where the damping is slightly less than the critical value is preferred for indicating instruments. Here's why:
- A slightly underdamped system might overshoot the final value by a very small amount, but it reaches the vicinity of the final value and settles much faster than an overdamped system.
- The small overshoot in a slightly underdamped system is usually quick and easily observable, allowing the user to quickly read the final steady value.
- Overdamping makes the pointer movement sluggish, delaying the measurement process.
Therefore, being slightly underdamped provides a good balance between speed of response and stability, leading to the best results for practical indicating instruments.
Important Questions from Damped Free Vibration
When there is reduction in amplitude over every cycle of vibration, then the body is said to have
A single degree of freedom system, having mass of 1 kg and stiffness of 10 kN/m is at rest. It is subjected to an impulsive force of magnitude 5 kN for 10-4 seconds. The amplitude (in mm) of the resulting free vibration is
A vehicle suspension system consists of a spring and a damper. The stiffness of the spring is 3.6 kN/m and the damping constant of the damper is 400Ns/m if the mass is 50Kg find damping factor and damped natural frequency respectively are
Which of the following statements are TRUE for damped vibrations?
P. For a system having critical damping, the value of the damping ratio is unity and the system does not undergo a vibratory motion.
Q. Logarithmic decrement method is used to determine the amount of damping in a physical system.
R. In case of damping due to dry friction between moving surfaces resisting force of constant magnitude acts opposite to the relative motion.
S. For the case of viscous damping, drag force is directly proportional to the square of relative velocity.
A suspended mass of 10 kg completes 40 oscillations in 20 seconds in a single-degree damped vibrating system. The stiffness of the spring is approximately _________.
