### 1.6 Degrees of damping LO (i)

If no frictional forces act on an oscillator (e.g. mass-spring system, simple pendulum system, etc.), then it will oscillate indefinitely.
In practice, the amplitude of the oscillations decreases to zero as a result of friction. This type of motion is called damped harmonic motion. Often the friction arises from air resistance (external damping) or internal forces (internal damping).

### 1.6.1 if the motion is x= x0 sin(ωt), the following are the x vs t graphs for 2 periods, as an illustration of the damping.

### 1.6.1.1 No damping

when b=0.0 no damping, system oscillates forever without coming to rest. Amplitude and thus total energy is constant

### 1.6.1.2 Light damping

when b=0.1 very lightly damp, system undergoes several oscillations of decreasing amplitude before coming to rest. Amplitude of oscillation decays exponentially with time.

### 1.6.1.3 Critical damping

when b=2.0, critically damp system returns to equilibrium in the minimum time, without overshooting or oscillating about the equilibrium position amplitude.

### 1.6.1.4 Heavy damping

when b=5.0, very heavy damp, system returns to equilibrium very slowly without any oscillation

### 1.6.2 a more typical starting position, is x= x0 cos(ωt), the following are the x vs t graphs for 2 periods, as an illustration of the damping.

### 1.6.2.1 No damping

when b=0.0 no damping, system oscillates forever without coming to rest. Amplitude and thus total energy is constant

### 1.6.2.2 Light damping

when b=0.1 very light damping, system undergoes several oscillations of decreasing amplitude before coming to rest. Amplitude of oscillation decays exponentially with time.

### 1.6.2.3 Critical damping

when b=2.0 critically damp, system returns to equilibrium in the minimum time, without overshooting or oscillating about the equilibrium position amplitude.

### 1.6.2.4 Heavy damping

when b=5.0 very heavy damp, system returns to equilibrium very slowly without any oscillation.

## 1.6.3 Model:

1. Run Sim
2. http://iwant2study.org/ospsg/index.php/84