# Springs

The physics of simple springs in their different types, helical and beam forms. The simplest is cantilever beam. There are a lot of applications of springs in everyday life. In our models we employ them to great effect. This page looks at the fundamentals.

### Spring Types

#### Cantilever Beam

where

E = Youngs modulus [Nm-2]

I = area moment of inertia [m4]

l = length [m]

#### Beam fixed at each End

where

E = Youngs modulus [Nm-2]

I = area moment of inertia [m4]

l = length [m]

#### Simply Supported Beam

where

E = Youngs modulus [Nm-2]

I = area moment of inertia [m4]

l = length [m]

#### Helical Springs

where

k = stiffness [Nm-1]

G = shear modulus [Nm-2]

d = wire diameter [m]

D = mean coil diameter [m]

n = number of turns

#### Axial Load on a Rod

where

E = Youngs modulus [Nm-2]

A = cross sectional area [m2]

l = length [m]

#### Tapered Rod with Axial Load

where

E = Youngs modulus [Nm-2]

D,d = end diameters [m]

l = length [m]

#### Quarter-Elliptic Laminated Leaf Spring

where

E = Youngs modulus [Nm-2]

n = number of leaves

b = width of leaves [m]

t = thickness of leaves [m]

l = span [m]

#### Semi-Elliptic Laminated Leaf Spring

where

E = Youngs modulus [Nm-2]

n = number of leaves

b = width of leaves [m]

t = thickness of leaves [m]

l = span [m]

### Hooke’s Law

Hooke’s Law states that, in a linear system, the restoring force is proportional to the displacement of the body, acting in a direction as to restore equilibrium.

### Mechanical Shock Absorber

The mechanical shock absorber is a mechanical device designed to smooth out or dampen a sudden shock impulse and dissipate kinetic energy. The shock absorber turns kinetic energy into thermal energy within the working fluids of system.