simple harmonic motion

conditions for shm

acceleration is directly proportional and in the opposite direction to displacement

two examples of simple harmonic systems

simple pendulum

mass-spring system

what is a simple harmonic system

a system which oscillates with simple harmonic motion

why does the angle of displacement for a simple pendulum have to be less than 10°

small angle approximation is used for the derivation of a formula

damping

The dissipation of energy from an oscillating system. The consequence is that the amplitude of oscillation will decrease. Damping occurs when a force opposes the system’s motion.

three main types of damping

light, critical, heavy

light damping/under-damping

energy is gradually removed from the system and the amplitude of oscillations slowly decreases.

critical damping

reduces the displacement of an oscillating object to its equilibrium position in the quickest time possible and without further oscillation

heavy damping/over-damping

the system is damped more than required to stop the oscillations. It takes longer for the system to return to equilibrium than for critical damping.

free vibrations

Oscillations that are not caused by a driver.

An object will naturally oscillate at its natural frequency.

They occur when no external force is continuously acting on the system

forced vibrations

where a system experiences an external driving force which causes it to oscillate

driving frequency

frequency of the driving force

what happens when the driving frequency is equal to the natural frequency of a system

resonance occurs

resonance

the amplitude of oscillations of a system drastically increase due to gaining an increased amount of energy from the driving force

use of damping

to decrease the effects of resonance

as the degree of damping increases…

resonant frequency and maximum amplitude decrease

peak of maximum amplitude becomes wider