Simple Harmonic Motion Overview

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Questions and Answers

Match the following terms related to Simple Harmonic Motion (SHM) with their correct descriptions:

Period (T) = Proportional to the square root of length (l) Total Mechanical Energy (E) = Constant throughout the oscillation Maximum Kinetic Energy (KE) = Occurs at the equilibrium position Maximum Potential Energy (PE) = Occurs at maximum displacement (amplitude)

Match the following mathematical expressions with their correct meanings in SHM:

KE = ½mv² = Kinetic energy formula PE = ½kx² = Potential energy formula T = 2π√(l/g) = Period of a simple pendulum φ = Phase constant determining initial conditions

Match the following types of oscillations with their characteristics:

Damped Oscillations = Amplitude decreases over time Forced Oscillations = External periodic force applied Equilibrium Position = Maximum velocity occurs here Resonance = Amplitude of response depends on frequency of force

Match the following descriptions with the concepts in SHM:

Phase Constant (φ) = Shifts the sinusoidal wave horizontally Frequency of External Force = Influences amplitude in forced oscillations Kinetic Energy at Amplitude = Zero at maximum displacement Potential Energy at Equilibrium = Minimum at the midpoint of motion Signup and view all the answers

Match the following aspects of motion with their corresponding behavior in SHM:

Velocity at Equilibrium = Maximum velocity Energy Conservation in SHM = Sum of KE and PE is constant Amplitude in Damped Motion = Decreases until the system comes to rest Amplitude in Forced Motion = Depends on external frequency Signup and view all the answers

Match the following terms related to Simple Harmonic Motion (SHM) with their definitions:

Restoring Force = Force that returns an object to its equilibrium position Amplitude = Maximum displacement from the equilibrium position Period (T) = Time for one complete oscillation Frequency (f) = Number of oscillations per unit time Signup and view all the answers

Match the following equations with their corresponding physical quantities in SHM:

F = -kx = Hooke's Law x = A cos(ωt + φ) = Equation of Displacement v = -Aω sin(ωt + φ) = Equation of Velocity a = -Aω^2 cos(ωt + φ) = Equation of Acceleration Signup and view all the answers

Match the following examples of SHM with their corresponding systems:

Mass-spring system = Oscillation of a mass attached to a spring Pendulum = Swinging motion of a pendulum Tuning fork = Vibrations producing sound waves AC Circuits = Oscillations in current or voltage in circuits Signup and view all the answers

Match the results of changes in a mass-spring system's properties with their effects on the period (T):

Increasing mass (m) = Increases the period (T) Increasing spring constant (k) = Decreases the period (T) Decreasing mass (m) = Decreases the period (T) Decreasing spring constant (k) = Increases the period (T) Signup and view all the answers

Match the following terms related to the characteristics of SHM with their properties:

Equilibrium Position = Net force on the object is zero Angular Frequency (ω) = Related to frequency by ω = 2πf Restoring Force = Proportional to displacement from equilibrium Frequency and Period = Reciprocals of each other Signup and view all the answers

Match the following types of oscillation with their descriptions:

Simple Pendulum = Undergoes small oscillations approx. SHM Mass-Spring System = Depends on mass and spring constant AC Circuits = Oscillations in current and voltage Waves = Motion described using SHM principles Signup and view all the answers

Match the following characteristics of SHM with their corresponding effects on motion:

Sinusoidal Motion = Displacement, velocity, and acceleration vary sinusoidally Equilibrium Force = Always directed towards the equilibrium position Frequency (f) = Number of cycles per second Amplitude = Maximum extent of oscillation Signup and view all the answers

Match the following descriptions of oscillatory motion with their key variables:

T = 2 * π * √(m/k) = Relation between period, mass, and spring constant a = -Aω^2 cos(ωt + φ) = Acceleration as a function of time v = -Aω sin(ωt + φ) = Velocity as a function of time x = A cos(ωt + φ) = Position as a function of time Signup and view all the answers

Flashcards

Simple Pendulum Period

A simple pendulum's period (T) is directly proportional to the square root of its length (l) and inversely proportional to the square root of gravitational acceleration (g). This relationship is expressed as: T = 2π√(l/g)

Energy Conservation in SHM

The total mechanical energy (E) remains constant throughout the oscillation, which is the sum of kinetic energy (KE) and potential energy (PE).

Maximum KE in SHM

The maximum kinetic energy (KE) occurs at the equilibrium position, where the velocity is highest. At this point, all energy is in motion.

Maximum PE in SHM

Maximum potential energy (PE) occurs at the maximum displacement (amplitude). This is where the object is furthest from equilibrium, meaning the most energy is stored.