{ shm simple harmonic motion. simply put, simple harmonic motion is a motion ‘back and forth’...

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Simple Harmonic Motion

Simply put, simple harmonic motion is a motion ‘back and forth’ away from and back to equilibrium

In SHM, the motion is caused by a restoring force, proportional to displacement.

SPRINGSApplied force F

results in ‘displacement’or change in the spring’s length: x

The amount of force applied to different springs to cause the same x is different

It depends on ‘stiffness’.k – spring constant, characterizes the spring’s stiffness.

Where is the restoring (net) force at its maximum?

Where is the restoring force = 0?

Where is the displacement maximum?

Where is displacement = 0?

Where is the acceleration = max?

Where is acceleration = 0?Where is v = max / 0?

SHM

The object is moving constantly moving about a position of equilibrium (unstrained length in this example under the influence of a restoring force. The restoring force is proportional to displacement.

Hooke’s Law for an ideal spring

FR – restoring force of a spring is proportional to displacement (stretch / compression) and is opposite the direction of x

Example

A 420-g block is attached to the end of a horizontal ideal spring and rests on a frictionless surface. The block is pulled so that the spring stretches for 2.1cm relative to its unstrained length. When the block is released, it moves with an acceleration of 9.0 m/s2. What is the constant of the spring?

PendulumHow does restoring force change? What does it depend on?

Critical thinking

Imagine a ball bouncing on the floor constantly returning to the same height (no energy loss = magic!).

Would this be considered an SHM?

Explain.

In SHM, there is a linear proportion between F and xFor an ideal spring, amplitude will not affect linear proportion.For a pendulum, the angle cannot exceed 15 degrees

For small angles

Characteristics of SHM

Characteristics of SHMA – amplitudeT – periodf – frequency

A pendulum with a mass of 0.100 kg was released. The string traces an angle of 14.0° between it’s farthest positions from equilibrium. The bob of the pendulum returns to its lowest point every 0.10 s.

What is the amplitude? (in degrees)

What is its period?

What is its frequency?

ANALOGY – reference circle

Two 50.0 g spheres are used in two oscillating systems: pendulum and mass-spring.

How will the period of oscillation change if the spheres are replaced with more massive samples?

How will the periods change if the systems are taken from the Earth to the moon?

Would the situation change in the mass-spring system if the spring was hung vertically?

This is the equilibrium position.There is no restoring force.

In order to create a restoring force, we need to either stretch or compress the spring. Then,

Rotational motion

Rotational motion

Can the amplitude equation be?

Critical thinking

Imagine a ball bouncing on the floor constantly returning to the same height (no energy loss = magic!).

What is happening with ME of the ball?

Energy transfer?

Energy transfer?

Energy transfer?