Chapter 17: Oscillations

What is the defining equation for SHM?

What is the defining equation for SHM?

a=(-)ω²x

What is the proportionality relationship between displacement and acceleration?

directly proportional

What is the gradient of an acceleration-displacement graph equal to?

-ω² (- (angular frequency)²)

What is an 'isochronous' oscillator?

An oscillator with a period/frequency that is not dependent on amplitude.

How can you infer that an oscillator is 'isochronous' from a displacement-acceleration graph?

=>if the gradient is a straight line (which it is), then the angular velocity is constant

=>because angular velocity is 2π/t (or 2πf) then the period/frequency is constant, regardless of amplitude

Summarise PAG 10.1 - Investigating factors affecting SHM

1.Attach the ball bearing to the string and attach this to the clamp stand as shown in the diagram below.

2. Adjust the length l, which is from where the string is attached to the clamp stand to the centre of the ball bearing, until it is 1.0 m using the metre ruler.

3. Wait until the pendulum bob stops moving completely, then place the fiducial marker directly underneath the bob. This represents the centre of oscillations and will make it easier to count how many oscillations the pendulum has undergone.

4. Pull the pendulum bob to the side slightly and let it go so that it is oscillating with a small amplitude and in a straight line.

5. As the pendulum passes the fiducial marker, start the stopwatch and count the time taken for it to complete 10 full oscillations.

6. Take two more readings of the time period for 10 oscillations and calculate a mean.

7. Reduce the length l by 10 cm and repeat the last 3 steps of the procedure. 8. Repeat the last step until the length l is 0.2 m.

What is the velocity at the amplitude of an oscillation?

zero

What is the velocity at the equilibrium position of an oscillation?

at a maximum

What is the acceleration of an oscillator at the amplitude of an oscillation

at a maximum but inverted because a ∝ -x

When do you use x = Acosωt?

When an Oscillation is starting from an amplitude

When do you use x = Asinωt?

When an Oscillation is starting from equilibrium position

How do you calculate the velocity of an oscillation?

v = ±ω√(A²-x²)

At the equilibrium position, (when t=0), what does the equation 'v = ±ω√(A²-x²)' turn into?

vₘₐₓ=ωA

Is TOTAL energy constant for an object moving in SHM?

yes

What is the kinetic energy at the amplitude of an oscillation?

zero

What type of energy is at the amplitude of an oscillation?

gravitational potential energy

How much energy is stored at the amplitude of an oscillation?

Zero gravitational potential energy and Maximum kinetic energy

Does the object in oscillation at the equilibrium position have any potential energy?

No

Draw an energy-displacement graph for the kinetic and potential energy during an oscillation (+show the total energy )

=> kinetic energy looks like an 'n' shape with maximum kinetic energy at x=0 (equilibrium position) and minimum kinetic energy at amplitudes

=> potential energy looks like a 'u' shape with minimum potential energy at x=0 (equilibrium position) and maximum potential energy at amplitudes

What are the two types of energy in a spring mass system (horizontal oscillation)?

Kinetic energy and elastic potential energy (no gravitational energy as its not vertical so its radius from the earths centre doesn't change)

In a spring-mass system, which type of energy is at a maximum at the amplitudes?

Elastic potential energy

How does conservation of energy play in a spring-mass system?

The kinetic energy of the glider on the spring-mass system must be equal to the difference between the total energy and elastic potential energy.

What is damping?

When an external force acts on an oscillator and has the effect of reducing the amplitude of an oscillation

Name two types of damping

light and heavy

What is LIGHT damping?

Light damping is when the amplitude of the oscillator gradually decreases over time

What is HEAVY damping?

when amplitude decreases significantly over time and period of oscillations increases.

What happens to kinetic energy in damping?

transferred to other energy stores

What is a free oscillation?

when a system oscillates without any external forces

What do you call the frequency of a free oscillation?

natural frequency

What is a forced oscillation?

Oscillations that occur when a system is made to oscillate by a periodic external force

What do you call the frequency of a forced oscillation?

driving frequency

When does resonance occur?

When driving frequency = natural frequency

What happens to the amplitude of an oscillation when there is resonance?

amplitude drastically increases (could cause system to break if not damped)

what is exponential decay (in terms of damping)?

when a system decreases exponentially over time

when does the greatest possible transfer of energy occur in SHM?

at the resonant frequency (amplitude of forced oscillation is maximum)

explain 4 observations of the damping graph

=> light damping - max. amplitude occurs at natural frequency of forced oscillator

=> as amount of damping increases , amplitude of vibration at any frequency decreases

=> max. amplitude occurs at lower frequency than natural frequency

=> peak on graph becomes flatter and broader