7.3 Pendulums

• The period (T) of a simple pendulum is given by the formula: T = 2π√(L/g)
• What are the two primary forces acting on a simple pendulum?

  Gravity and tension
• The gravitational acceleration (g) is approximately 9.8 m/s²
• What is a simple pendulum an idealized system of?

  Point mass and string
• The small angle approximation assumes the angle of displacement is less than 10 degrees.


  True
• What are the two primary forces acting on a simple pendulum?

  Gravity and tension
• The tangential component of gravity is Fg_t = mg sin(θ), which acts along the swing arc.


  True
• Match the parameter with its unit:

  Angular Acceleration (α) ↔️ rad/s²

  Gravitational Acceleration (g) ↔️ m/s²

  Length (L) ↔️ m

  Angular Displacement (θ) ↔️ rad

  Period (T) ↔️ s
• Increasing the length of a pendulum will increase its period.


  True
• The period of a pendulum depends on two key factors
• How does increasing gravitational acceleration affect the period of a pendulum?

  Decreases the period
• What is the relationship between the period and the length of a simple pendulum?

  Directly proportional
• The small angle approximation assumes the angle of displacement is less than 10 degrees.


  True
• Gravity provides the restoring force that drives the pendulum back towards its equilibrium
• The tension in the string balances the radial component of gravity.


  True
• The tension in the string of a pendulum balances the radial component of gravity and any centripetal force
• Match the force acting on a pendulum with its role:

  Gravity ↔️ Restoring force (tangential component)

  Tension ↔️ Maintains circular motion
• The equation of motion for a simple pendulum shows that it undergoes simple harmonic motion.


  True
• What does α represent in the equation of motion for SHM in a pendulum?

  Angular acceleration
• What is the formula for the period of a simple pendulum?

  T = 2π√(L/g)</latex>
• The unit of frequency is Hertz
• The frequency of a pendulum is the inverse of its period
• Match the property with its unit:

  Period ↔️ s

  Frequency ↔️ Hz
• The period of a pendulum is directly proportional to the square root of its length.


  True
• The frequency of a pendulum is the reciprocal of its period.


  True
• What is the formula for the period of a pendulum?

  $2π√(L / g)$
• Increasing gravitational acceleration decreases the period of a pendulum.


  True
• Damped harmonic motion occurs when an oscillating system loses energy due to damping forces
• In simple harmonic motion, energy is conserved, but in damped harmonic motion, energy is lost due to damping
• The mass of a physical pendulum is distributed throughout a rigid body
• The period of a physical pendulum is given by $2π√(I / mgd)$, where d is the distance to the center of mass.


  True
• The length of a pendulum is measured in meters
• The frequency of a pendulum with a period of 2.02 seconds is approximately 0.5 Hz.
• What are the two key parameters that affect the motion of a simple pendulum?

  Length and gravitational acceleration
• The small angle approximation assumes the displacement angle is typically less than 10 degrees for accuracy.


  True
• Match the force with its role in a simple pendulum:

  Gravity ↔️ Provides restoring force

  Tension ↔️ Maintains circular path
• Steps to derive the equation of motion for a simple pendulum

  1️⃣ Consider the tangential component of gravity

  2️⃣ Apply Newton's Second Law

  3️⃣ Use the small angle approximation

  4️⃣ Simplify the equation

  5️⃣ Obtain the equation of motion
• The period (T) of a simple pendulum is given by the formula: 2π√(L/g)
• Match the parameter with its description:

  Length (L) ↔️ Distance from suspension point to mass

  Mass (m) ↔️ Point mass at the end of the string

  Gravitational Acceleration (g) ↔️ Local gravitational force

  Period (T) ↔️ Time for one complete oscillation
• The magnitude of gravity acting on a pendulum is given by: Fg = mg