All Flashcards
How do you start oscillations in a mass-spring system for an experiment?
To initiate oscillation in a mass-spring system, displace the mass vertically from its equilibrium position and release it, ensuring no additional forces act on the mass.
Aside from a mass-spring system, what's another example of an oscillating system you can investigate?
A mass swinging from side to side at the end of a long string, known as a simple pendulum.
Describe the displacement-time graph for simple harmonic motion.
The displacement-time graph of an object in simple harmonic motion is sinusoidal, resembling a sine or cosine wave, indicating periodic motion.
What achievement in radio communication did Count Marconi accomplish following Hertz's discoveries?
Count Maroni successfully transmitted messages across the Atlantic using radio waves, around 15 years after Hertz's initial research.
In simple harmonic motion, in which direction is the system always accelerated?
The system is always accelerated towards the centre of the motion, known as the equilibrium position.
How is simple harmonic motion (SHM) related to uniform circular motion (UCM)?
Simple harmonic motion (SHM) can be derived from uniform circular motion (UCM). If you project the circular motion on one axis, the resulting motion is SHM. The angular frequency (ω) in SHM corresponds to the rate of rotation in UCM, establishing a direct correlation between the two types of motion.
How is the time period (T) related to the angular frequency (ω) in simple harmonic motion?
The time period (T) is the reciprocal of the frequency (f) and is related to the angular frequency (ω) by T = 2π/ω.
How does angular frequency (ω) relate to the acceleration in simple harmonic motion?
In simple harmonic motion, angular frequency (ω) is related to the period (T) and determines the acceleration (a) at a given displacement (x) by the formula a = -ω²x. The acceleration is directly proportional to the displacement and inversely proportional to the square of the period.
How is simple harmonic motion related to circular motion?
The relationship between circular motion and simple harmonic motion (SHM) can be visualized by projecting the shadow of an object moving in a uniform circular motion onto a line or plane. This shadow moves back and forth in SHM, akin to a pendulum's swing.
Define Hooke's Law.
Hooke's Law states that the restoring force (F) in a spring is proportional to its displacement (x). It's given by F = -kx, where k is the spring constant.
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 is the effect of gravity on an object in free fall?
The object accelerates downwards at approximately 9.8 m/s².
What happens when a projectile is launched at an angle?
The initial velocity has both horizontal and vertical components, affecting the range and maximum height.
What is the effect of increasing the launch angle (below 45 degrees) on the range of a projectile?
The range increases.