Oscillations in the spring-mass system Maximum speed, maximum kinetic energy Maximum force, maximum acceleration

Will the period change if the amplitude changes? period

Frequency and period are not dependend on the amplitude! What are the implications for musical instruments? Pitch is not dependent on how much the string is plucked (for example)

Does the period depend on the mass? Which force is acting on both masses? Which acceleration does each mass experience? The smaller mass accelerates at a higher rate: it is faster to move through the cycle. It will oscillate at a smaller period (faster).

Properties of the spring and period stiff soft Large spring constant k1 Small spring constant k2 Large k means high acceleration High acceleration means a cycle is completed fast High k low period

Factors influencing the period: InfluencePeriodFrequency Mass m  Stiffness k  Amplitude ANo influence

Frequency and Period

Simple harmonic motion What is influenced by the amplitude?

What happens if energy gets lost due to friction? A) the frequency decreases B) the period decreases C) the amplitude decreases D) all of the above

The amplitude decreases. Frequency and period stay the same. Damped harmonic motion

Example Clink of a coffee cup

Example Finger flicking Short, hard to assign pitch

Driven oscillator Slow driving frequency: f 0 < f Mass moves in rhythm with the driver.

Driven oscillator Fast driving frequency: f 0 > f The mass is practically not moving.

Driven oscillator Resonance: f 0 = f Amplitude grows very much!

Amplitude versus driving frequency Resulting amplitude Driving frequency Natural frequency of oscillator

The shocks of an automobile are springs. Which of the following would be desirable? A) resonance with the bumps on the road, and little damping B) high damping and high spring constant C) high damping and very low spring constant D) resonance with the bumps on the road, and high damping

A) resonance with the bumps on the road, and little damping

B) high damping and high spring constant One bump, high spring constant, medium damping One bump, high damping, medium spring constant Several bumps, high damping, medium spring constant Answer C: similar effects

D) resonance with the bumps on the road, and high damping Multiple bumps

Examples of other oscillators Pendulum (small amplitude) L

Examples of other oscillators Air-filled piston m L A Atmospheric Pressure P 0 P0P0 m Atmospheric Pressure P 0 P 0 +p m Atmospheric Pressure P 0 P 0 -p F=pA

Examples of other oscillators Helmholtz Resonator L V A