Oscillations

What is displacement

Distance from equilibrium position

What is amplitude

Maximum displacement

What is time period

Time taken for a full oscillation

What is frequency

Number of oscillations per unit time

What is phase difference

How out of sync two waves/oscillations are (as a fraction of a single oscillation in radians)

What is angular frequency

Rate of change of angular position

What is simple harmonic motion

• Acceleration directly proportional to displacement

• Acceleration acts away from equilibrium position

• And in the opposite direction of displacement

• Given by -\omega^2x

What type of oscillation is shm and what does this mean

• isochronous

• Period is independent of amplitude

Method of investigating shm (inaccurately)

• set oscillator into motion (e.g. mass on spring or pendulum)

• Record time taken for a full oscillation

• Since shm is isochronous amplitude doesnt affect time period

• Fiducial marker (clear reference point) as a point for stopping and starting the timer (typically at equilibrium position)

How can we improve the accuracy of investigating shm

• Take time taken for 10 full oscillations and find a mean

• Record the oscillator so that using video stills we can deduce a time that isnt affected by human reaction time

Analysing shm

• the two equations used for displacement

• When each one is used

• x=A\sin\omega t

• x=A\cos\omega t

• Sin is used when starting at equilibrium

• Cos is used when starting at amplitude

Where does max velocity happen

At equilibrium position

What is the value of velocity at amplitude

Zero

Where does max accel occur

At amplitude

What is accel at equilibrium

Zero

If \displaylines{v=\pm\omega\sqrt{A^2-x^2}\\ }

Then what the eqn for maximum velocity

v=\omega A

How is energy transferred in shm

Between KE and PE

Where is max KE

At equilibrium

Where is max PE

At amplitude

What happens to the total energy in shm

It is conserved

What is damping

Where amplitude decreases over time due to energy loss from resistive forces

3 Types of damping and how it affects the oscillation

• Light damping - amplitude decreases exponentially

• Heavy damping - amplitude decreases dramatically

• Critical damping - object stops oscillating before a single oscillation

Examples of when the 3 types of damping occur

Light - naturally (in air)

Heavy - in water

Critical - in treacle

What is a free oscillation

Where there are no external forces acting on the system and it is at its natural frequency

What are forced oscillations

When a periodic driving forces causes a particular frequency

When does resonance occur

When driving freq = natural freq

What happens at resonance

• rapid amplitude increase

• If no damping, amplitude increases until the system fails

• When damping increases, amplitude decreases at all frequencies

What happens when driving frequency increases past point of resonance

Amplitude will decrease from this point onwards

• Method for investigating resonance

• What stops the system from failing

• How to improve the accuracy of amplitude measurement

• mass between two strings attached so oscillator generators

• Mm ruler places parallel to system

• Slowly increase driver frequency from zero

• So that mass oscillates with increasing amplitude

• Max amplitude when driving frequency = natural frequency

• Amplitude will decrease as driving frequency increases past resonance

• System should not fail due to light damping from air

• System should be recorded so that amplitude can be determined from video stills due to it being difficult as the mass oscillates