All Flashcards
Define simple harmonic motion and specify the conditions for its occurrence.
Simple harmonic motion (SHM) is oscillatory motion where an object swings around an equilibrium point with restoring force proportional to displacement. It occurs under uniform circular motion resemblance or when restoring forces follow Hooke's Law, typically at small amplitudes where linearity holds.
What was Joseph Fourier's contribution to understanding oscillations?
Joseph Fourier, an 18th-century French mathematician and physicist, developed Fourier analysis, a method to express complex oscillations as sums of simple sine waves. This fundamental work underpins modern spectral analysis of waveforms, including sound.
How do you construct a square-wave from sine waves?
A square-wave can be approximated by summing sine waves at odd harmonic frequencies, scaled by 1/n. Mathematically, add sine functions (1/n)*sin(nx) for odd integers n. More terms yield a closer approximation.
In the function y = sin(x) + 1/3 sin(3x) + 1/5 sin(5x) + …, identify the pattern of the terms.
The series' terms take the form (1/n)sin(nx) for odd n values. It's a Fourier series example, decomposing a periodic function into harmonic components.
Define 'isochronous' in the context of oscillations.
In oscillations, 'isochronous' refers to the property where each cycle takes the same amount of time to complete, regardless of amplitude.
What happens to the amplitude of a real oscillating system over time?
The amplitude of a real oscillating system decreases over time as it transfers energy to the environment and eventually stops.
In simple harmonic motion, is the displacement from equilibrium positive or negative when above the equilibrium position?
Displacement is considered positive if above the equilibrium position, given that the upward direction is chosen as positive.
What is the maximum displacement of the oscillator from the equilibrium position called?
Amplitude (x0). Remember, it's not the distance from one extreme to the other and does not have a sign.
Calculate the frequency in hertz of a heart beating 65 times per minute.
To find the frequency in hertz (Hz), divide the number of beats per minute by 60 seconds. Frequency = 65 beats/minute ÷ 60 seconds/minute = 1.0833 Hz (approximately 1.08 Hz).
What type of graph is produced by data logger software in a mass-spring system experiment?
The data logger software will produce a time-displacement graph, showing how the displacement of the mass varies over time, indicating simple harmonic motion.
What are the steps to analyze 2D motion?
- Break the motion into x and y components. 2. Analyze x and y components separately. 3. Time is the same for both x and y.
What are the steps to solve projectile motion problems?
- Identify initial velocity and launch angle. 2. Calculate initial x and y components of velocity. 3. Analyze vertical motion using kinematic equations with a = -g. 4. Analyze horizontal motion with constant velocity. 5. Use time to connect x and y components.
What are the steps to find the resultant vector?
- Break down vectors into their x and y components using trigonometry (sin and cos). 2. Combine vector components. 3. Find the overall vector using Pythagorean theorem and trigonometry.
What are the differences between scalar and vector quantities?
Scalar: Magnitude only (e.g., speed, mass, distance). Vector: Magnitude and direction (e.g., velocity, force, displacement).