6.1.3 Simple Harmonic Systems Mr Smith DHS 16/17 6.1.3 Simple Harmonic Systems

- Spring stiffness (N/m) Mass-Spring System One of the most common SHM systems is the mass on a spring. The factors affecting the oscillations of the system are; - Mass (kg) - Spring stiffness (N/m)

Mapping the motion It is important you know how to map the motion of the SHM systems to the graphs that we discussed in the previous topic. for example, at which point is maximum displacement, velocity and acceleration… In which case where is the maximum force in the spring. Max Displacement = Fully stretched/Fully compressed Max Velocity = Equilibrium Max acceleration = Fully stretched/Fully compressed Max Force = Fully stretched/Fully compressed

Simple Pendulum The next most common SHM system you will encounter is the simple pendulum. The factors effecting the time period of the simple pendulum are; - length of string - gravity Interestingly, the mass on the string does not affect the period of oscillation!!!! Test it.

Mapping the oscillations Again… you must be able to map the motion of the pendulum to the graphs and physical quantities, x, v, a and F. Max Displacement = A/C Max Velocity = Equilibrium/B Max acceleration = A/C Max Force = A/C A C B Remember, the displacement and acceleration are directly proportional… but in the opposite directions!!

Energy of Simple Harmonic Systems You need to know how the energy of the two systems varies over the oscillations… The energy present in the systems is: - Kinetic - Gravitational Potential - Elastic Potential (mass-spring)

Mass-Spring Where is the kinetic energy maximum? Energy Ek & Ep Mass-Spring Where is the kinetic energy maximum? Equilibrium because the velocity is maximum! Where is the gravitational potential maximum? At the top since it is the highest point! Where is Elastic potential a maximum? At the top and bottom since the spring is stretched and compressed to a max at both points!

Simple Pendulum Where is the kinetic energy maximum? Energy Ek & Ep Simple Pendulum Where is the kinetic energy maximum? Equilibrium because the velocity is maximum! Where is the gravitational potential maximum? At the two max displacements since it is the highest point!

Mapping the energy changes Learn this graph by heart!!

The more damping, the faster it comes to a stop! These systems are free of any resistive forces in theory… but in practice as we know, there are resistance forces in nature. Air resistance is the biggest contributor to this resistive force and thus… Total energy is not conserved!!! If you set a pendulum swinging in the lab, or a mass spring bouncing up and down… it would of course eventually come to an end. This slowing down the oscillations to a stop and removing the energy from the system, is known as damping! The more damping, the faster it comes to a stop!

Make sure you know the energy changes (and graph) for this topic. To Summarise… All equations in the previous topic 6.1.2 SHM are applicable to these systems, as they are Simple Harmonic. The systems themselves are important to know how their motion is mapped and the Time periods of both are very important for the final exam!!! Make sure you know the energy changes (and graph) for this topic. And be aware of what damping is and how it can be used in the real world!

Equations from this topic 6.1.3 SHS

Practice the questions on the link from the website… Any problems, come see me!