6.1 Periodic motion

• What is the defining characteristic of periodic motion?

  Repeats after a period
• A ball thrown in the air is an example of periodic motion.

  False
• In SHM, the acceleration is proportional to the displacement
• The frequency of SHM is equal to 1/T.


  True
• The angular frequency (\(\omega\)) in SHM is related to the frequency (f) by the equation \(\omega = 2\pi f\)
• What is the defining characteristic of periodic motion?

  Repeats after a period
• What type of motion is Simple Harmonic Motion (SHM)?

  Periodic motion
• Projectile motion is an example of SHM.

  False
• What does the amplitude (A) in SHM represent?

  Maximum displacement
• The acceleration in SHM is always directed towards the equilibrium position.


  True
• Match the SHM equations with their descriptions:

  Displacement (x) ↔️ Position relative to equilibrium

  Velocity (v) ↔️ Rate of change of displacement

  Acceleration (a) ↔️ Rate of change of velocity
• The displacement of an object in SHM with \( \omega = 5 \) rad/s and \( \phi = 0 \) at \( t = 2 \) seconds is approximately -0.0839 meters.


  True
• For a mass-spring system to exhibit SHM, the spring must obey Hooke's Law
• What is the restoring force in a mass-spring system that leads to SHM?

  F = -kx
• Where is the potential energy in SHM maximum?

  At maximum displacement
• What is the maximum potential energy of a mass-spring system with \( k = 200 \) N/m and \( A = 0.05 \) m?

  0.25 J
• In Simple Harmonic Motion (SHM), the total energy is the sum of potential energy (PE) and kinetic energy (KE), and it remains constant if there is no damping
• The maximum kinetic energy in SHM occurs at the equilibrium position.


  True
• What is the time interval between repetitions in periodic motion called?

  Period
• In Simple Harmonic Motion (SHM), the acceleration is proportional to the displacement and directed towards the equilibrium position.


  True
• In SHM, the velocity equation is $v =$$- A\omega \sin(\omega t + \phi)$
• What is the displacement of a mass-spring system at $t =$$2$ s with $A =$$0.1$ m, $\omega =$$5$ rad/s, and $\phi =$$0$?


  $- 0.0839$ m
• The displacement of an object in SHM at \(t = 2\) seconds is approximately -0.0839 meters.
• Match the example of SHM with its description:

  Mass-Spring System ↔️ Restoring force proportional to displacement

  Simple Pendulum ↔️ Restoring torque proportional to angular displacement
• The restoring force in the mass-spring system ensures the mass oscillates around the equilibrium position in SHM.


  True
• Both the mass-spring system and the simple pendulum exhibit constant period and amplitude in SHM if conditions are met.

  True
• What is the equation for potential energy in SHM?

  $PE =$$\frac{1}{2} k x^{2}$
• The total mechanical energy in SHM remains constant if there is no damping.


  True
• Match the type of damping with its description:

  Underdamping ↔️ Oscillates with decreasing amplitude

  Critical Damping ↔️ Returns to equilibrium quickly without oscillation

  Overdamping ↔️ Returns slowly to equilibrium without oscillation
• Resonance occurs when the driving frequency matches the natural frequency of an oscillating system.

  True
• Give an example of resonance in a physical system.

  Mechanical vibrations
• In periodic motion, the period is always constant
• What type of motion is Simple Harmonic Motion (SHM)?

  Periodic
• Arrange the key parameters of SHM in order of their definitions:

  1️⃣ Period (T): Time for one complete oscillation

  2️⃣ Frequency (f): Number of oscillations per second

  3️⃣ Amplitude (A): Maximum displacement from equilibrium
• What does the variable 'A' represent in SHM equations?

  Amplitude
• The phase constant in SHM determines the initial velocity of the object at t=0.

  False
• Match the SHM variable with its equation:

  Displacement (x) ↔️ \( x = A \cos(\omega t + \phi) \)

  Velocity (v) ↔️ \( v = -A\omega \sin(\omega t + \phi) \)

  Acceleration (a) ↔️ \( a = -A\omega^2 \cos(\omega t + \phi) \)
• In SHM, the acceleration is proportional to the object's displacement
• Match the examples of SHM with their properties:

  Pendulum ↔️ Restoring torque proportional to angular displacement

  Mass-Spring System ↔️ Restoring force proportional to displacement
• The angular frequency (\(\omega\)) is related to the period (T) by the equation \(\omega = \frac{2\pi}{T}\), which also equals 2\pi f