waves test

Describe the potential energy and kinetic energy within a pendulum, and the relationship between amplitude and energy.

At the Highest Points the pendulum momentarily stops before changing direction, so its velocity is 0. Here, Potential Energy is at its maximum and Kinetic Energy is zero.

At the Lowest Point (Equilibrium): The pendulum is moving at its fastest speed and is at its lowest height. Here, Kinetic Energy is at its maximum and Potential Energy is at its minimum relative to the rest of the swing.

Increasing the amplitude means pulling the pendulum back to a higher starting position. Higher release height increases its initial gravitational potential energy, which increases the total mechanical energy of the system.

Of the three things you can change, (length, mass, angle), which one has the biggest effect on the pendulum, and why?

Length has the biggest effect on the period of a simple pendulum;

The period of a simple pendulum depends on string length and gravity. Increasing the length creates a longer path and reduces the restoring acceleration, increasing the time it takes to complete a cycle. the mass has no effect because gravity accelerates all masses at the same rate. Changing the angle (for small angles, typically under 15°) has a negligible effect on the period.

Describe the restoring force acting on a pendulum in motion.

The restoring force pulls the pendulum bob back toward its equilibrium position (the bottom center).

Source of the Force: It is the component of gravity acting perpendicular to the tension of the string.

At maximum amplitude, the restoring force is strongest. At the center (equilibrium), the net restoring force drops to zero.

Interpret Harmonic motion graphs

equilibrium in position v time is 0; find amplitude (total/2); period=time for one full cycle, peak to peak distance; frequency =1/period in hertz

Three examples of oscillating systems

A Playground Swing: It moves continuously back and forth around a central equilibrium point powered by gravity and momentum.

Grandfather clock: uses a pendulum as an oscillator

A Guitar String: Plucking the string pulls it out of position, and the string's elasticity acts as a restoring force, causing rapid back-and-forth vibration at a fixed frequency to create sound.

Relate Newton’s 1st law to the cycle of a pendulum

Newton’s First Law (Inertia): An object in motion stays in motion unless acted upon by a net force.

As a pendulum falls from its peak toward the center, gravity accelerates it. When it reaches equilibrium, the net restoring force momentarily becomes zero. However, due to inertia, the pendulum bob refuses to stop at the bottom and continues moving upward to the opposite side until gravity slows it down and pulls it back.

Discern whether two oscillators are in-phase or out-of-phase based on their graphs.

Two waves or oscillators are in-phase when their crests and troughs align at the exact same times. Their phase difference is 0’.

Two waves are out-of-phase when their peaks do not align. If one oscillator reaches a peak at the exact moment the second reaches a trough, they are 180’ phase ("completely out-of-phase").

Period frequency formula

T=1/f f=1/T

analog v digital signals

Both are used to transmit data or information over distances using electromagnetic waves or electrical signals.

Analog Signals: Continuous waves that vary smoothly in amplitude and frequency (like vinyl records or landline audio). They are susceptible to noise, degradation, and static over long distances.

Digital Signals: Discrete signals consisting of binary values. They are more reliable over long distances because noise can be filtered out easily without degrading the underlying data.

explain law of relflection

The Law of Reflection states that when a light ray hits a smooth surface, the angle of incidence is equal to the angle of reflection.

Both angles are measured relative to the Normal line (an imaginary perpendicular line to the surface at the point of contact).

Explain index of refraction and why light bends when it crosses into new media.

Index of Refraction (n): A value that measures how much a medium slows down light compared to its speed in a vacuum (n = c / v). Higher n values mean light travels slower in that material.

Why Light Bends: As light crosses a boundary at an angle into a medium with a different optical density, one side of the light wave front changes speed before the other side. This difference in speed causes the direction of the wave front to pivot (bend).

Air to Water (Fast to Slow): Light bends toward the normal line.

Water to Air (Slow to Fast): Light bends away from the normal line.

interpret ray diagrams

Reflection Diagrams:

• Incident Ray: The incoming ray approaching the mirror.

• Reflected Ray: The ray bouncing off the mirror.

• Normal Line: The dashed vertical line perpendicular (90’) to the surface.

• Angle measurements start at 0’ at the normal line and expand outward toward the rays.

Refraction Diagrams:

• Identify the boundary line between the two media (e.g., Air vs. Water).

• Draw the perpendicular normal line where the incident ray strikes the surface.

• Track the angle changes: If the ray bends closer to the normal inside the second medium, the second medium has a higher index of refraction and a slower speed of light.

linear motion

one dimensional movement straight line single direction where restoring force moves system away from equilibrium

harmonic/periodic motion

repeating back and forth movement when restoring force pulls system back to equilibrium

oscillator

system that uses harmonic motion

pendulum

oscillating system with bob on string that swings back and forth

cycle

one full repetition back and forth

period

time it takes to complete one cycle

period of the pendulum = 2 cycles

frequency

number of cycles finished in one second, in hertz (Hz)

amplitude

size of oscillation, distance traveled from equilibrium, more amplitude = more energy

damping

decreased friction in system causing it to slow in speed

unstable system

restoring force pulls system away from equilibrium

stable system

restoring force pulls toward equilibrium

restoring force

gravity; equilibrium is maintained by it - pulls system back to it; often demonstrates harmonic motion

inertia

mass - when added: decreases natural frequency, system responds slower - lengthens period and shortens frequency, causes system to overshoot equilibrium

phase

degrees which describe location of oscillator in cycle

natural frequency

typical frequency of an oscillating system - may be used as a way to tell time

analog signal

original signal, curved, most accurate

digital signal

analog wave transmitted into binary (0 or 1 values - reconstructed wave)

refraction

light ray travels through different mediums/speeds - absorbtion and reemmition by each atom it hits slows light ray’s speed,causing bend (greater the difference of speed between materials, greater the bend) index refraction = speed in vacuum/speed in material

light rays bend toward normal from low n (index refraction) to high n

light rays bend away from normal from high n to low n