SHM

• acceleration is proportional to negative displacement
• characteristic equation of SHM is $a=$$\omega^2x$
• velocity is a maximum at the equilibrium and a minimum at the edges
• acceleration is a maximum at the edges and a minimum at equilibrium
• SHM is used for pendulums with under 10 degrees of a swing
• when finding the distance a pendulum swings, use mgh=1/2mv^2
• total energy is kinetic energy at equilibrium
• damping occurs when adding resistive forces in the opposite direction to velocity
• resonance is when a driving force is added in the same direction as velocity
• resonance occurs when the applied force has the same frequency as the natural frequency of the object
• the velocity graph is the gradient function of the displacement graph (gradient of x is v)
• resonance causes maximum energy transfer
• stationary waves only occur at resonant frequency
• characteristic feature of SHM is that the time period is independent of amplitude
• the object in SHM experiences a restoring force which is proportional to displacement and towards equilibrium
• light damping is where the amplitude gradually decreases by a small amount each oscillation
• critical damping is when the amplitude reduces to 0 within 1/2 a cycle without oscillating
• heavy damping is when the amplitude reduces slower than critical damping but without oscillations
• light damping causes strong resonance with a lower amplitude
• heavy damping causes resonance with a peak that is less sharp and at a lower amplitude
• no damping causes very sharp very high amplitude resonance
• Forced vibrations are oscillations when a system is driven by an external periodic force to vibrate at the frequency of the driving force