Oscillations

Simple harmonic motion definition

A restoring force that acts on an object towards the centre of equilibrium

terms in F=-kx

F= restoring force, K is a constant, x is distance from the equilibrium

What is the relationship between simple harmonic motion and displacement

Is directly proportional but in the opposite direction

terms in a=-w²x

a is acceleration, w= angular speed, x=displacement

Angular speed (w)

the angle an object moves through per unit time

What is the term A

The amplitude of oscillation

What are simple harmonic systems

systems that oscillate with simple harmonic motion

Simple pendulum definition

A small, dense bob of mass m hanging from a string l, which is attached to a fixed point

Resonance definition

Where the amplitude of oscillations of a system drastically increases due to gaining an increased amount of energy from the driving force

Applications of resonance

Instruments, Radio and a swing

When does Resonance occur?

when the driving frequency is equal to the natural frequency of the system

What can damping be used for

to decrease the effect of resonance

What is damping

where a force acts on an oscillating system and energy is lost from the system to its environment, leading to reduced amplitude of oscillation

How does the conservation of energy apply to an oscillating system

they cannot gain or lose energy unless there are any external force acting on it

Energy transfers in a simple harmonic motion system

Kinetic energy is transferred to potential energy and back as the system oscillates, the type of potential energy depends on the system

Energy at certain points of a system

At the amplitude of its oscillations the system will have the maximum amount of potential energy

As it moves towards the equilibrium position, theis potential energy is converted to kinetic energy so that at the centre of its oscillations the kinetic energy is at a maximum

then as the system moves away from the equilibrium again, the kinetic energy is transferred to potential energy until it is at a maximum again and this process repeats from one full oscillation

What happens in an undamped system

there are no external forces acting, therefore no energy is lost to the environment and so the total energy of the system remains constant

What happens in a damped system?

there is at least one external force acting, therefore some energy will be lost to the environment

What are free vibrations?

occur when no external force is continuously acting on the system, therefore the system will oscillate at its natural frequency

What are forced vibrations

where a system experiences an external driving force which causes it to oscillate

Light damping

This is also known as under-damping and is where the amplitude gradually decreases by a small amount each oscillation

Critical damping

This reduces the amplitude to zero in the shortest possible time

Heavy damping

Also known as over-damping, and is where the amplitude reduces slower that with critical damping

How can the plastic deformation of a ductile material can be used to reduce the amplitude of oscillations?

energy is used to deform the material which decreases the kinetic energy of the system and so the amplitude of oscillations decreases

A ductile material

one that can undergo a large amount of plastic deformation before fracturing