Simple Harmonic Motion How will this driver survive?

The Importance of Springs The suspension on the car will act to reduce the force on the driver as he lands How do automotive engineers know how big or how stiff the spring should be? Experiments!

The Importance of Springs When the car lands, the spring will be compressed Once it reaches maximum compression, it will expand It will expand beyond the equilibrium point, then compress once more These oscillations act with decreasing amplitude until the spring is once more at rest

Simple Harmonic Motion Simple harmonic motion (SHM) is a periodic motion that is neither driven nor damped We are going to simulate SHM using a small mass and a series of springs

The Maths! Using Hooke’s Law F = -kx and Newton’s Second Law F = ma we can define an expression for the system ma = -kx With some simplification and rearrangement we arrive at As frequency is the reciprocal of the period of oscillation we can write

Simple Harmonic Motion How does an increase in mass alter the period of oscillation? Describe the relationship between the period of oscillation and the mass on the spring. Why is this a good simulation of a car suspension? In what ways could it be improved? This system is clearly damped (otherwise it would oscillate forever) – what forces are causing this damping?

Pendulums and Bobs A pendulum, as found on a grandfather clock or in 90s cult TV show Gladiators, also undergoes Simple Harmonic Motion The theory is similar, however different properties affect the period of oscillation

A Few Questions How does an increase in mass alter the period of oscillation? Describe the relationship between the period of oscillation and the angle of displacement. Describe the relationship between the length of the pendulum and the period of oscillation. In what ways could this practical be improved? This system is clearly damped (otherwise it would oscillate forever) – what forces are causing this damping?

Gladiators The Pendulum in Gladiators was designed and built by engineers Assuming the period of oscillation was 15 seconds how long should the pendulum have been to allow this to happen? The pendulum was obviously not this long – how did the engineers ensure that it moved accordingly?