Simple Harmonic Motion Quiz

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Questions and Answers

What is the maximum displacement of the particle in SHM?

  • 2 cm
  • 1 cm
  • 4 cm (correct)
  • 3 cm

What is the acceleration of the particle when it is at a distance of 1 cm from its mean position?

  • 1 cm/s^2
  • 2 cm/s^2
  • 4 cm/s^2
  • 3 cm/s^2 (correct)

What is the velocity of the particle when it is at a distance of 2 cm from the mean position?

  • 1 cm/s
  • 3 cm/s
  • 2 cm/s (correct)
  • 4 cm/s

Which of the following relationships is correct between the acceleration ‘𝛽′ and the displacement ‘y’ of a particle involved in simple harmonic motion?

<p>β = -5 𝑦 (A)</p> Signup and view all the answers

In the simple harmonic motion described by the equation x = 0.25 cos(π/8 t), what is the amplitude of the motion?

<p>0.25 m (C)</p> Signup and view all the answers

What is the angular frequency of the simple harmonic motion described by the equation x = 0.25 cos(π/8 t)?

<p>π/8 rad/s (C)</p> Signup and view all the answers

What is the period of the simple harmonic motion described by the equation x = 0.25 cos(π/8 t)?

<p>16 s (D)</p> Signup and view all the answers

What is the displacement of the object after 2.0 seconds in the simple harmonic motion described by x = 0.25 cos(π/8 t)?

<p>0.125 m (B)</p> Signup and view all the answers

What is the period of the oscillation of a 326-g object attached to a spring with a total energy of 5.83 J?

<p>0.250 s (A)</p> Signup and view all the answers

What happens to the period of a pendulum when mercury is drained from a hollow sphere?

<p>It increases (B)</p> Signup and view all the answers

What defines free oscillation?

<p>Oscillation without external interference (A)</p> Signup and view all the answers

What is the correct unit for angular frequency (ω)?

<p>rad/s (C)</p> Signup and view all the answers

If a block weighing 4 kg stretches a spring by 0.16 m, what will be the effect on the spring's constant when a 0.5 kg block is hung?

<p>It remains the same (D)</p> Signup and view all the answers

Which of the following is a characteristic of forced or driven oscillation?

<p>Requires external energy input (C)</p> Signup and view all the answers

What is the total energy of a system undergoing simple harmonic motion if the maximum speed is calculated to be 1 m/s?

<p>5.83 J (A)</p> Signup and view all the answers

What is true about the maximum acceleration of an object in simple harmonic motion?

<p>It is dependent on the spring constant and mass (B)</p> Signup and view all the answers

What does a greater spring constant indicate about a spring?

<p>It resists compression more effectively. (A)</p> Signup and view all the answers

How does a stiffer spring affect car stability during cornering?

<p>Reduces weight transfer. (C)</p> Signup and view all the answers

Which equation provides the relationship between the spring constant and mass in harmonic motion?

<p>k = mω^2 (D)</p> Signup and view all the answers

What is the effect of a softer suspension system on car performance?

<p>Increases the risk of reduced stability. (D)</p> Signup and view all the answers

What happens to the car's position when a stiffer spring is used?

<p>The car is displaced higher from the ground. (D)</p> Signup and view all the answers

In the context of Hooke's law, what does a higher spring constant imply?

<p>Higher restoring force at displacement. (B)</p> Signup and view all the answers

What is the relationship between mass (m) and angular frequency (ω) in terms of spring constant?

<p>k = mω^2 (D)</p> Signup and view all the answers

How does stiffer suspension potentially affect driving comfort?

<p>Decreases comfort by making the ride harsher. (A)</p> Signup and view all the answers

What primarily determines the natural frequency of an object?

<p>Various factors including size, shape, and material properties (C)</p> Signup and view all the answers

Why is it important for aircraft designers to consider natural frequency in wing design?

<p>To prevent violent flapping that can be dangerous (A)</p> Signup and view all the answers

What phenomenon occurs when an external driving force's frequency is close to an object's natural frequency?

<p>Resonance (D)</p> Signup and view all the answers

What happens to a swing's time period if a person standing in the swing sits down?

<p>The time period decreases (B)</p> Signup and view all the answers

Which concept best explains the movement of tectonic plates?

<p>Oscillatory Motion (D)</p> Signup and view all the answers

How does a change in altitude affect the time period of a pendulum?

<p>It has no effect regardless of height (B)</p> Signup and view all the answers

If a guitar string is tensioned, how is its natural frequency affected?

<p>Increases with higher tension (A)</p> Signup and view all the answers

What is the effect of damping on the oscillation of a system?

<p>It decreases the amplitude of oscillation over time (B)</p> Signup and view all the answers

What happens to the time period of a swing when Miss Dema stands up? Why?

<p>It increases because the center of mass rises. (C)</p> Signup and view all the answers

If Miss Dema swings at a higher altitude, what effect does it have on the time period?

<p>It increases due to a decrease in gravitational force. (C)</p> Signup and view all the answers

What effect does having Miss Dema's friend on the swing have on the time period?

<p>The time period increases due to added mass. (A)</p> Signup and view all the answers

What is the correct equation for the time period of a simple pendulum?

<p>T = 2π√(l/g) (D)</p> Signup and view all the answers

What happens to the time period of a pendulum when it is taken to the Moon?

<p>It increases due to decreased gravitational force. (D)</p> Signup and view all the answers

How is the spring constant calculated from the force applied and displacement?

<p>k = F/x where k is spring constant, F is force, x is displacement. (A)</p> Signup and view all the answers

What is the relationship between potential energy and position in simple harmonic motion?

<p>Potential energy varies quadratically with position. (D)</p> Signup and view all the answers

In the equation T = 2π√(m/k), what does 'm' represent?

<p>Mass of the body in motion. (B)</p> Signup and view all the answers

Which of the following accurately distinguishes between periodic and oscillatory motion?

<p>Oscillatory motion is always periodic, but periodic motion may or may not be oscillatory. (C)</p> Signup and view all the answers

Which of the following is NOT a characteristic of oscillatory motion?

<p>Amplitude of oscillation always remains constant over time. (A)</p> Signup and view all the answers

Which of the following examples represents simple harmonic motion?

<p>The motion of a pendulum bob. (D)</p> Signup and view all the answers

A bird flapping its wings circles around a clock tower. What type of motion is the flapping of its wings?

<p>Periodic but not oscillatory (C)</p> Signup and view all the answers

In the following examples, which represent periodic motion but NOT simple harmonic motion? (Select all that apply)

<p>The rotation of the Earth about its axis. (A), Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lowest point. (C), A freely suspended bar magnet displaced from its N-S direction and released. (D)</p> Signup and view all the answers

What is the key difference between simple harmonic motion and other types of periodic motion?

<p>Simple harmonic motion involves a restoring force proportional to the displacement and opposite in direction. (D)</p> Signup and view all the answers

Which of the following is an example of a system that exhibits simple harmonic motion?

<p>A swinging pendulum (C)</p> Signup and view all the answers

Which of the following statements about the restoring force in simple harmonic motion is TRUE?

<p>The restoring force is always directed towards the equilibrium position. (D)</p> Signup and view all the answers

Flashcards

Simple Harmonic Motion (SHM)

A type of periodic motion where the restoring force is proportional to displacement from equilibrium.

Displacement in SHM

The position of a particle from its mean or equilibrium position at a given time.

Maximum Velocity (V)

The highest speed of a particle in SHM, calculated using V = ωA, where A is amplitude and ω is angular frequency.

Acceleration in SHM (β)

The acceleration of a particle in SHM related to its displacement by the equation β = -ω²y.

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Angular Frequency (ω)

The rate of oscillation measured in radians per second, related to the frequency of motion.

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Amplitude (A)

The maximum displacement from the mean position in SHM.

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Time Period (T)

The time it takes to complete one full cycle of SHM, calculated as T = 1/frequency.

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Frequency (f)

The number of complete cycles of SHM in one second, the inverse of the time period.

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Periodic Motion

Motion that repeats after a definite time interval, can be along any path.

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Oscillatory Motion

Back and forth motion around a fixed point within a definite time interval.

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Relation of Oscillatory to Periodic Motion

Every oscillatory motion is periodic, but not all periodic motions are oscillatory.

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Characteristic of Oscillatory Motion

Tends to return to equilibrium, restoring force is proportional to displacement.

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Time Period

The time taken for one complete cycle of motion in periodic processes.

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Frequency

The number of cycles of motion that occur in one second.

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Restoring Force

The force that brings an oscillating body back to its equilibrium position.

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Time Period of Swing

The time taken for one complete oscillation of a swing.

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Effect of Standing on Time Period

If Miss Dema stands, the time period decreases due to a lower center of mass.

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Effect of Height on Time Period

Swinging at a higher altitude increases the time period as potential energy rises.

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Adding Mass to Swing

If Miss Dema’s friend joins, the time period increases due to greater mass.

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Hooke's Law

Relationship describing the force exerted by a spring as proportional to its displacement.

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Time Period of Simple Pendulum

T = 2π√(l/g), where l is length and g is gravity's acceleration.

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Spring Constant Calculation

Spring constant k can be calculated from force F and displacement x: k = F/x.

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Spring Constant (k)

A measure of a spring's stiffness; greater k means stiffer spring.

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Potential Energy (PE) in springs

Given by PE = 1/2 kA² cos²(ωt), depends on spring constant and amplitude.

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Kinetic Energy (KE) in springs

Given by KE = 1/2 m(ωA sin(ωt))², varies with spring motion.

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Stability in cars

Controlled by the spring constant; stiffer springs improve stability.

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Car Suspension

System using springs to support a vehicle's weight and absorb shocks.

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Body Roll

The tilting motion of a vehicle's body during cornering.

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Soft vs Stiff Springs

Soft springs allow more compression, leading to body roll; stiff springs minimize it.

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Total Energy in SHM

The sum of potential and kinetic energy in a simple harmonic oscillator is constant.

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Maximum Velocity (v_max)

The highest speed reached during the motion in SHM.

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Maximum Acceleration (a_max)

The highest acceleration in simple harmonic motion, proportional to amplitude.

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Natural Angular Frequency (ω)

The angular frequency at which a system oscillates when not driven by external forces.

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Natural Frequency

The frequency at which a body vibrates when disturbed from equilibrium.

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Factors Affecting Natural Frequency

The size, shape, and material properties of an object influence its natural frequency.

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Resonance

Increased amplitude when driving frequency is close to natural frequency.

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Damping Constant (b)

A measure of how much the oscillation reduces over time due to resistance.

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Effects of Natural Frequency in Aviation

Aligning wing frequency with engine frequency can cause dangerous vibrations.

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Impact of Ice Melting on Pendulum Period

Melting ice will change the mass of the pendulum bob, affecting its oscillation period.

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Swinging Position Impact on Period

Standing up on a swing increases the period due to the change in mass distribution.

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Tectonic Plate Movement and Resonance

The interaction of tectonic plate movements can be explained by resonance phenomena.

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Study Notes

Summary of Oscillatory Motion

  • Periodic Motion: A motion that repeats after a specific time interval.
  • Oscillatory Motion: A motion in which a body repeatedly moves back and forth about a fixed point.
  • Oscillatory Motion is always periodic but Periodic motion is not always oscillatory
  • Examples of Periodic Motion: pendulum bob, ball rolling back and forth in a round bowl, motion of clock hands
  • Examples of Oscillatory Motion: swinging pendulum, to and fro motion of atoms in a substance, vibrations of strings in a guitar.
  • Examples of Periodic Motion but not Oscillatory Motion: Uniform circular motion, motion of planets.

Simple Harmonic Motion (SHM)

  • Definition: SHM is a type of oscillatory motion where the restoring force is directly proportional to the displacement from the equilibrium position and is directed towards the equilibrium position.
  • Characteristics of SHM:
    • Restoring force is proportional to displacement.
    • Restoring force is opposite in direction to displacement.
    • The energy remains conserved.

Displacement Equation of SHM

  • Equation: x = A sin(ωt + φ) or x = A cos(ωt + φ), where:
    • x is the displacement from the equilibrium position at time t.
    • A is the amplitude (maximum displacement).
    • ω is the angular frequency (rad/s).
    • t is the time.
    • φ is phase constant (initial phase).

Velocity in SHM

  • Equation: v = ±ω√(A² - x²)
  • This shows velocity is maximum at equilibrium position.

Acceleration in SHM

  • Equation: a = -ω²x
  • Acceleration is directly proportional to the negative of the displacement from the mean position. Maximum at extreme position.

Time Period and Frequency

  • Time period (T): The time taken for one complete oscillation.
  • Frequency (f): The number of oscillations per unit time. f = 1/T
  • Angular frequency (ω): ω = 2πf = 2π/T

Energy in SHM

  • Potential Energy (PE): PE = ½ kx²
  • Kinetic Energy (KE): KE = ½ mv²
  • Total Energy (TE): TE = PE + KE = ½kA²
  • At the extreme positions: PE is maximum, KE is zero, and TE is constant.
  • At the equilibrium position: PE is zero, KE is maximum, and TE is constant.

Phase

  • Phase Constant (φ): Initial phase of the motion.
  • Phase: wt + φ, expresses the position and direction of motion

Resonance

  • Resonance: The phenomenon of increased amplitude of oscillation when the driving force frequency is close to the natural frequency of the oscillator.
  • Aircraft and Resonance: Aircraft designers avoid resonance to stop violent wing flapping caused by forced oscillations.

Period of a Simple Pendulum

  • Formula: T = 2π√(L/g), where:
    • T is the period.
    • L is the length of the pendulum.
    • g is the acceleration due to gravity.

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