Simple Harmonic Motion Concepts
16 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the value of the spring constant 𝑘 for the spring in the scenario?

  • 0.20 [N/m]
  • 1.00 [N/m]
  • 9.81 [N/m]
  • 3.14 [N/m] (correct)

What is the period of oscillation 𝑇 for the weight after being released?

  • 2.00 [s]
  • 4.00 [s]
  • 0.50 [s]
  • 1.00 [s] (correct)

What is the angular velocity 𝜔 calculated for this oscillation?

  • 6.28 [rad/s] (correct)
  • 1.57 [rad/s]
  • 12.56 [rad/s]
  • 3.14 [rad/s]

What is the amplitude of the oscillation 𝐴 for this system?

<p>0.20 [m] (B)</p> Signup and view all the answers

What is the displacement at time 𝑡 = 100 [s] calculated using the given function?

<p>0.190 [m] (A)</p> Signup and view all the answers

What is the theoretical maximum speed of the weight as it passes through the equilibrium position O?

<p>0.39 [m/s] (D)</p> Signup and view all the answers

Which equation correctly expresses the displacement from the equilibrium position O as a function of time 𝑦(𝑡)?

<p>𝑦(𝑡) = 0.200 cos(6.28𝑡) (A)</p> Signup and view all the answers

What does the negative sign in the force equation −𝑚𝑔 + 𝑘𝑥0 = 0 signify?

<p>Restoring force acting upward (B)</p> Signup and view all the answers

What is the maximum speed of the object undergoing simple harmonic motion with amplitude 0.2 m?

<p>1.26 m/s (A)</p> Signup and view all the answers

Which equation correctly represents the velocity of the object at any time t?

<p>v(t) = -1.26 sin(6.28t) (D)</p> Signup and view all the answers

What is the maximum magnitude of acceleration for the object with an amplitude of 0.2 m?

<p>7.90 m/s² (D)</p> Signup and view all the answers

What is the angular frequency of the object undergoing simple harmonic motion given the force applied?

<p>1.4 rad/s (C)</p> Signup and view all the answers

What is the correct expression for the acceleration as a function of time?

<p>a(t) = -7.89 cos(6.28t) (B)</p> Signup and view all the answers

What is the period of the simple harmonic motion for the object with a mass of 2.0 kg?

<p>4.4 s (B)</p> Signup and view all the answers

When the object is at point P (1.0 m from the center), what is the force acting on it?

<p>-4.0 N (D)</p> Signup and view all the answers

What is the speed of the object when it passes through the center of vibration?

<p>2.4 m/s (D)</p> Signup and view all the answers

Flashcards

Spring constant (k)

A measure of a spring's stiffness. It relates the force needed to stretch or compress the spring to the distance stretched or compressed.

Period of oscillation (T)

Time taken for one complete oscillation (cycle).

Angular velocity (ω)

Rate of change of angle during oscillation, measured in radians per second.

Amplitude (A)

Maximum displacement from the equilibrium position during oscillation.

Signup and view all the flashcards

Displacement function (y(t))

Mathematical description of an object's position at any time during simple harmonic motion.

Signup and view all the flashcards

Simple Harmonic Motion (SHM)

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

Signup and view all the flashcards

Frequency (f)

Number of oscillations per unit of time (e.g., cycles/second).

Signup and view all the flashcards

Equilibrium position

The center point of oscillation, where the net force on the object is zero.

Signup and view all the flashcards

Velocity (v) in SHM

Velocity of an object in simple harmonic motion (SHM) is given by the function: 𝑣 = −𝜔𝐴 sin 𝜔𝑡. The speed varies sinusoidally, reaching a maximum (𝑣max = 𝜔𝐴) when sin 𝜔𝑡 = 1

Signup and view all the flashcards

Maximum speed (𝑣max)

The greatest speed an object reaches during its simple harmonic motion, calculated by multiplying the angular frequency (𝜔) by the amplitude (𝐴).

Signup and view all the flashcards

Acceleration (a) in SHM

Acceleration in SHM is described by the formula: 𝑎(𝑡) = −𝐴𝜔2 cos 𝜔𝑡. It's also sinusoidal and varies in relation to displacement from the equilibrium position.

Signup and view all the flashcards

Maximum acceleration (𝑎max)

The maximum acceleration of an object in simple harmonic motion,calculated by multiplying the square of the angular frequency (𝜔) by the amplitude (𝐴).

Signup and view all the flashcards

Angular Frequency (𝜔)

A measure of how quickly an object oscillates in simple harmonic motion during a given time interval (measured in radians per second).

Signup and view all the flashcards

Restoring Force in SHM

The force that pulls the object back towards its equilibrium position. In SHM, the restoring force is directly proportional to the displacement from equilibrium and is always directed towards the equilibrium position.

Signup and view all the flashcards

Period (T) in SHM

The time it takes for one complete oscillation in simple harmonic motion.

Signup and view all the flashcards

Speed at Point P (SHM)

The speed of an object at point P (a specific displacement) in SHM is determined from the formula 𝑣=𝜔√(𝐴2-𝑦2) where 𝐴 is amplitude and 𝑦 is displacement from the centre position.

Signup and view all the flashcards

Study Notes

Simple Harmonic Motion

  • Spring Constant (k): Calculated using k = mg/xo, where m is mass, g is acceleration due to gravity, and xo is the displacement.
  • Period of Oscillation (T): Calculated as T = 1/f, where f is frequency. Also equal to 2π /ω.
  • Angular Velocity (ω): Calculated as ω = 2πf or ω = √(k/m).
  • Amplitude (A): The maximum displacement from the equilibrium position. In this example it is 0.2m.
  • Displacement Function (y(t)): Expressed as y(t) = Acos(ωt), where A is amplitude and ω is angular frequency (angular velocity), and t is time.

Displacement at Specific Time

  • Displacement at t = 100s: Calculated using y(t) = Acos(ωt), with the calculated values for A and ω.

Velocity

  • Velocity at Equilibrium: Velocity is maximum when the object is passing through the equilibrium position. Calculated using Vmax = ωA.

Acceleration

  • Maximum Acceleration: Maximum acceleration is given by Amax = ω²A

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

Physics 2 Assignment - Week 4 Simple Harmonic Motion PDF

Description

This quiz covers essential concepts of simple harmonic motion, including calculations for spring constant, period, angular velocity, amplitude, and displacement function. Dive into the relationships between velocity and acceleration in oscillatory motions. Test your understanding of the key principles and formulas governing this fundamental physics topic.

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser