1.1. To understand the energy transformations To understand the energy transformations which take place during simple harmonic which take place during simple harmonic motionmotion

Book Reference : Pages 44-45Book Reference : Pages 44-45

If we consider an If we consider an idealideal pendulum.... pendulum....

Which form of energy will it have when it is Which form of energy will it have when it is displaced from the equilibrium position at displaced from the equilibrium position at one of the two extremes of oscillationone of the two extremes of oscillation

Which form of energy will it have when it is Which form of energy will it have when it is moving through the equilibrium positionmoving through the equilibrium position

Which form(s) of energy will it have during the Which form(s) of energy will it have during the rest of the cycle?rest of the cycle?

How does the total energy change during the How does the total energy change during the whole cycle?whole cycle?

It has the “potential to fall” and so gravitational It has the “potential to fall” and so gravitational potential energy (Epotential energy (Epp))

It is moving and so it will definitely have kinetic It is moving and so it will definitely have kinetic energy (Eenergy (Ekk). At the equilibrium point it cannot ). At the equilibrium point it cannot “fall further” so only kinetic“fall further” so only kinetic

Everywhere else it is moving and has the Everywhere else it is moving and has the potential to fall further & so the energy is a potential to fall further & so the energy is a combination of Ecombination of Ep p && EEkk

The total energy remains unchanged. It The total energy remains unchanged. It alternates between being all Ealternates between being all Epp, a mixture of both , a mixture of both & all E& all Ekk

How will this apply to an How will this apply to an idealideal horizontal SHM horizontal SHM system based around springs?system based around springs?

How about if the spring arrangement were How about if the spring arrangement were vertical?vertical?

Exactly the same, apart from the potential energy Exactly the same, apart from the potential energy would be elastic potential energy stored in the would be elastic potential energy stored in the spring rather than gravitationalspring rather than gravitational

Same conversion between potential and kinetic Same conversion between potential and kinetic energy and back again. However, this time the energy and back again. However, this time the potential would be a combination of potential would be a combination of gravitational and elasticgravitational and elastic

Sketch a graph of the total energy, Ep & Ek on the Sketch a graph of the total energy, Ep & Ek on the same axis as the pendulum oscillates between same axis as the pendulum oscillates between AA

+A-A

Ek

Ep

Total Energy

Energy

displacement

If we use information about the energy in the If we use information about the energy in the system, and a few “bits” of other information, system, and a few “bits” of other information, what other things are we likely to be able to what other things are we likely to be able to find?find?

Think about the alternative way of approaching Think about the alternative way of approaching SUVAT type problems... For example the SUVAT type problems... For example the skateboarder questionskateboarder question

We can equate the conservation of energy (ideal We can equate the conservation of energy (ideal world)world)

At extremes At extremes A total energy = EA total energy = Epp and E and Ekk = 0 = 0

Passing through the equilibrium point total Passing through the equilibrium point total energy = Eenergy = Ek k and Eand Ep p = 0= 0

In between Total energy = EIn between Total energy = Epp + E + Ekk

This will typically allow us to solve problems with This will typically allow us to solve problems with a range of information (Ea range of information (Ekk = ½mv = ½mv22), (Gravitational ), (Gravitational EEpp = mg = mgh) and h) and perhapsperhaps the potential energy the potential energy stored in a spring (Estored in a spring (Epp = ½F = ½FL)L)

A system in simple harmonic motion is A system in simple harmonic motion is being damped when energy is being being damped when energy is being “lost” from the system in oscillation“lost” from the system in oscillation

Most obvious is air resistance and Most obvious is air resistance and friction in the pivot pointfriction in the pivot point

Next Practical : Spring with “Next Practical : Spring with “parachuteparachute” ” experimentexperiment