2. 1© Manhattan Press (H.K.) Ltd. Forced oscillation Resonance Resonance 7.8 Forced oscillation and resonance Experiments for forced oscillation and resonance Experiments for forced oscillation and resonance

3. 2 © Manhattan Press (H.K.) Ltd. Forced oscillation 7.8 Forced oscillation and resonance (SB p. 286) Forced oscillation - oscillating system is driven by a periodic force (e.g. playing a swing)

4. 3 © Manhattan Press (H.K.) Ltd. Forced oscillation 7.8 Forced oscillation and resonance (SB p. 286) For simple pendulum Natural frequency (f o ) - depends on length ( ) For loaded spring Natural frequency (f o ) - depends on force constant (k) of spring and mass (m) of load

5. 4 © Manhattan Press (H.K.) Ltd. Forced oscillation 7.8 Forced oscillation and resonance (SB p. 286) The simple pendulum or loaded spring (oscillating systems) can be forced to oscillate by an external periodic force. Driving frequency - frequency of external periodic force - equals frequency of system

6. 5 © Manhattan Press (H.K.) Ltd. Forced oscillation 7.8 Forced oscillation and resonance (SB p. 286) Amplitude of oscillation - gradually increase (energy transfer is cumulative) At equilibrium, - rate of energy from driving force = rate of energy dissipated by damping force - amplitude becomes constant

7. 6 © Manhattan Press (H.K.) Ltd. Forced oscillation 7.8 Forced oscillation and resonance (SB p. 287) driving frequency closer to f o, - smaller damping - greater amplitude

8. 7 © Manhattan Press (H.K.) Ltd. Resonance 7.8 Forced oscillation and resonance (SB p. 287) Resonance - frequency of driving force = natural frequency of oscillating system - maximum energy is transferred to system - amplitude becomes the highest resonant frequency No damping: amplitude increases without limit With damping force (real cases): amplitude depends on degree of damping (energy transfer reaches dynamic equilibrium)

9. 8 © Manhattan Press (H.K.) Ltd. Resonance 7.8 Forced oscillation and resonance (SB p. 288) f << f o, oscillate nearly in phase with driving force f = f o, oscillate with a phase lag of  /2 behind driving force f >> f o, oscillate nearly out of phase with driving force

10. 9 © Manhattan Press (H.K.) Ltd. Experiments for forced oscillation and resonance 7.8 Forced oscillation and resonance (SB p. 289) Oscillation of bob provides periodic force, cones are forced to oscillate Until long pendulum out of phase with driver pendulum Until short pendulum in phase with driver pendulum

11. 10 © Manhattan Press (H.K.) Ltd. Experiments for forced oscillation and resonance 7.8 Forced oscillation and resonance (SB p. 289) Resonance occurs - length of cone = length of driver pendulum - the cone moves with largest amplitude and phase lag of  /2 to driver pendulum

12. 11 © Manhattan Press (H.K.) Ltd. End