Physics - Oscillations

Use faradays law and energy conservation to explain why the amplitude of the oscillation of the magnet reduces after time 6 seconds. [3] (light damping graph)

• as coil cuts the magnetic flux, an EMF is induced which gives a rise to current

• The current passes to the resistor which causes heating

• The energy lost through heating causes amplitude to decrease.

The amplitude of the oscillation of the plate is gradually increased beyond 8 mm the frequency is constant at one amplitude the sand is sent to loose contact with the plate for the plate when the sand first lose his contact with the plate state the position of the plate.

Above equilibrium position are at highest position.

State two conditions necessary for a mass to be undergoing simple harmonic motion

1. Acceleration proportional to displacement

2. Displacement and acceleration and opposite or acceleration directed towards a fixed point (the point being equilibrium position)

1. State and explain whether the oscillations of the trolley are heavily damped, critically damped or lightly damped.

2. Suggest the cause of damping

1. Lightly damped as amplitude gradually decreasing OR oscillations continue so light damping

2. Energy is lost (as heat) due to friction between wheels and surface OR air resistance on trolley.

The mass M is now suspended from two springs each identical to the figure and 3.1 as shown in figure 3.3.

Suggest and explain the change if any in the period of oscillation of the mass, a numerical answer is not required. [2]

• period decreases

• As (any point among these)

• Greater spring constant or stiffness

• Restoring force is greater (for any given extension)

• Acceleration is greater (for any given extension)

• Greater energy or maximum speed (for a given amplitude)

(As concept: when springs in parallel, k+k=2k, so larger spring constant, hence double stiffness hence half extend , (when in series, (1/k + 1/k )^-1=0.5 K less stiff so double extend).

F=kx, where F restoring force

ma = kx

mw²x = kx

mw² = k

k/m= 4\pi ² / T²

K inversely proportional to time period, so increasing spring, spring constant decreases period.

Relationship between amplitude and energy.

Total energy= 1/2mw²A²

So energy directly proportional to amplitude²

The oscillator is switched on. The frequency of oscillation of the oscillator is varied, keeping its amplitude constant.

At any given frequency, the amplitude of oscillation of trolley is constant.

Explain how this indicates that there resistive forces opposing the motion of the trolley. [2]

• oscillator supplies, energy continuously

• Without loss of energy, the amplitude would continuously increase.

(Remember if amplitude² directly proportional to Energy)

REMEMBER Energy is not only dependent on amplitude. If energy of oscillation is constant, it does not mean amplitude also has to be constant.

Energy = 1/2mw²A²

Amplitude can be changing and the mass or the angular frequency also can change to keep the energy constant.

The acceleration a of a oscillating object is related to the displacement x by the expression

a = -(g/L)x

Where g is the acceleration of freefall.

Explain how the expression shows that the object is undergoing simple harmonic motion. [3]

• acceleration is an opposite direction to displacement shown minus sign

• g/L is a constant

• Showing that acceleration is directly proportional to displacement x.

Show that the liquid column under goes s.h.m [2]

a = -kx where k is a constant

g and L are constants

So this shows a proportional to -x

Hence, s.h.m

State what is meant by displacement of the mass on the spring [1]

Distance from a (reference) point from a given direction

Describe without calculation the interchange between the potential and the kinetic energy of the oscillation in shm. [3]

• Sum of potential energy and kinetic energy remains constant

• When with maximum displacement from equilibrium potential energy energy, maximum kinetic energy is zero

• When at zero displacement from equilibrium kinetic energy is max and potential energy is 0.

State, by reference to simple harmonic motion, what is meant by angular frequency. [1]

The relation to the period by 2\pi / T and the frequency by 2\pi f.

Show that the load is undergoing simple harmonic motion. [3]

• displacement from equilibrium (2.0 cm) is proportional to the acceleration if load is in s.h.m

• Straight line shows that acceleration is directly proportional to displacement

• Negative gradient shows that acceleration and displacement in opposite directions

State one cause of the damping

Any of these causes

• friction between the liquid and the walls of tube

• Viscosity of liquid

• Friction within the liquid

• Viscous Drag

The effects of damping on Resonance

As the degree of damping increases

• The height of peak decreases (the height of the resonance peak decreases as damping increases because energy is dissipated more rapidly(Energy is constantly being lost (as heat, etc.), so not all the input energy can be stored in the system, reducing the maximum amplitude)

• The peak moves slightly to the left (Some of the driving energy is “wasted” overcoming resistive forces The system can’t respond as effectively at higher frequencies So the maximum amplitude now occurs at a slightly lower frequency)

• The peaks become less sharp (“Sharpness” means:

• How quickly amplitude drops as you move away from resonance

With low damping:

• Only frequencies very close to f_0 can build large amplitude

• So you get a sharp, narrow peak

With high damping:

• Oscillations die out quickly

• Energy doesn’t build up much at any frequency

When calculating the total energy using maximum kinetic energy (instead of mgh)

Always use the horizontal distance

E total= 1/2mw²A² (where A is max horizontal distance from equilibrium)