Harmonic Motion

Harmonic Motion

Warmup: A tennis ball is hit back and forth between two players. If it takes 2.3s for the ball to go from one player to the other,what are the period and frquency of the ball's motion?

Simple harmonic motion

• force pushing or pulling an object toward equilibrium is proportional to the displacement from equilibrium

• The previous force is called a restoring force

• What do you think might be an example of this?

Hooke's law

• F=kx

• springs force is proportional to its distance

• restoring force is within the spring itself

Amplitude

• Displacement from equilibrium

• Easily recognizable as a sine or cosine wave

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Amplitude problem

A mass moves back and forth in simple harmonic motion with and amplitude of .25 m and a period of 1.2 s. Through what distance does the mass move in 2.4 s?

Period of a mass on a spring depends on a couple factors

• varies inversely with spring constant- the higher the spring constant the shorter the time

• varies directly with mass- a higher mass means a longer period

•  $T=2\pi\sqrt{\frac{m}{k}}$  

• Notice that the equation does not factor in amplitude for the period, interestingly enough a greater amplitude, becuase it results in a greater restoring force, does not increase the time it takes to complete a cycle

Spring constant problem

A .22 kg air track cart is attached to a spring with a spring constant of 12 N/m and set into motion. What is the period of its oscillation?