Question

Please provide an example of a damped harmonic oscillator. They are more common than undamped or simple harmonic oscillators. What do you think there is any harmonic motion in the physical world that is not damped harmonic motion? Try to make a list of five examples of undamped harmonic motion and damped harmonic motion. Which list was easier to make? Why are the group of the peoples in general ordered to “route step” (walk out of step) across a bridge?

Answer 1

A simple pendulum swinging in air, is an example of a damped harmonic oscillator.

Any harmonic motion in physical world is mostly damped in nature. This damping effect is mainly due to frictioal forces acting due to any other systems that are in contact with the oscillator or in case of isolated system also, it is due to surrounding medium.

The energy of the oscillator is continuously transfered to its surroundings to compensate frictional effects. This is in support of law of conservation of energy.

Examples of undamped harmonic motion:

1. Simple pendulum attached to a friction less rigid support in vacuum

2. Excited tuning fork placed on frictionless support in vacuum.

3. Oscillations made by a spring-mass system with frictionless contact and support in vacuum.

4. Oscillations produced in a streached string with frictionless supports present in vacuum.

5. An LC circuit (having inductor and capacitor connected in series) connected to a power source with no internal resistance of the circuit.

The five examples described above, if observed carefully indicate ideal cases. These require ideal conditions such as frictionless supports, vacuum in case of mechanical systems (ex. 1 - 4) and circuit with no internal resistance (ex. 5). If the real world conditions are introduced instead the ideal conditions, the five systems listed above will act as examples of damped harmonic motion.

Examples of damped harmonic motion:

1. Simple pendulum attached to a rigid support in air

2. Excited tuning fork placed on a support in air.

3. Oscillations made by a spring-mass system in air.

4. Oscillations produced in a streached string present in air.

5. An LC circuit (having inductor and capacitor connected in series) connected to a power source.

In practice, the list of examples of undamped harmonic motion is difficult to prepare.

Every object will have its natual frequency with which it tries to oscillate when a force is appled on it. If the natural frequency of the obect is equal to the frequency of the applied force then the object oscllates with larges amplitudes. This condition is known as resonance.

When people such as soldiers march fast on a bridge, they will apply a force on the suface of a bridge at regular intervals of time, creating an applied frequency. If it matches with the natural frequency of the brigde, it leads to mechanical resonance leading to oscillate the bridge violantly with enhanced amplitudes which may collapse the bridge. To avoid such condition, people are asked to route step across bridges.