6.1.6

# Energy in Simple Harmonic Motion

Test yourself

## Conservation of Energy

Energy cannot be created or destroyed so the total energy of the system must be conserved. The amounts of kinetic and potential energy are able to change.

### Kinetic and potential energy

• Kinetic energy comes from movement:
• $KE=1/2mv^2$
• Gravitational potential energy comes from a gain in height:
• $GPE=mgh$
• Elastic potential energy comes from squashing or stretching a spring:
• $EPE=1/2kx^2$

### Total energy

• At any point in the cycle, the total energy must be the sum of all the other energies and it must remain constant.
• $E=KE+GPE+EPE=constant$
• In the centre of the oscillation, EPE is at a minimum and KE is at a maximum.
• At the top of the oscillation, KE is 0 and GPE and EPE are at a maximum.

## Damped Oscillations

In the real world friction acts on an oscillation object, this produces heat so reduces the amount of energy the object has. This will decrease the amplitude of the oscillations.

### Damping

• When an oscillation is damped the amplitude of the wave decreases but the period and the frequency remain the same.
• A damping force is any force which opposes the movement of the object.

### Types of damping

• If the damping on a system is small then the system is hardly affected, it will take a long time until you can see the amplitude reduce or the oscillations stop. This is under-damping.
• If the system has too much damping no oscillations will happen at all, the object will just slowly return to equilibrium. This is over-damping
• If the object returns to equilibrium as quickly as possible it has critical-damping.

### Critical damping

• Critical damping is very desirable as it reduces oscillations quickly and can avoid damage.
• In car suspension, critical damping is needed for a comfortable and safe ride.