C2 Damped Oscillations, SHM Energy and Resonance and Resonance in real-life

-Energy is dissipated due to work done on the oscillating system due to restive forces, i.e, air resistance and friction
-Energy is usually transferred in the form of heat.
-Damping causes a decrease in amplitude
W[r]=/(K.E+P.E)
work done by resistive force-->W[r]=/\K.E+/\P.E }sum of changes in P.E, K.E
damping graph img:
-For a system with a small amount of damping a.k.a under damping(or light damping in Qs) the period and frequency are nearly the same as for simple harmonic motion
-Critical damping is where the damping of an oscillator results in it returning as quickly as possible to its equilibrium position.
-Heavy damping a.k.a overdamping is where the amplitude reduces slower than with critical damping but also without any additional oscillations
Types of damping graphs img:
SHM Energy
-For any SHM system K.E is transferred to P.E and back as the system oscillates.
-The type of potential energy depends on the system.
shm energy graph img:
-At the amplitude the system will have maximum potential energy
-At equilibrium position K.E is maximum.
-The total energy of the system remains constant when the system is undamped
-The following graph shows the variation of energy with time.
energy-time graph img:
{Def:Resonance
-the frequency at which a system would oscillate if there were no driving force and no damping force(free oscillations) is called natural frequency
-The largest amplitude of oscillation is observed at natural frequency.
-The phenomenon of driving a system with a frequency equal to the system's natural frequency is called resonance.
Resonance in real-life

Musical instruments:
-flutes and musical glass causes air in them to resonate and causes a stationary sound wave
Radio:
-tuned to have the electric circuit resonate at the same frequency of broadcast frequency