Conditions for Simple Harmonic Motion

• What is simple harmonic motion (SHM)?


  A specific type of oscillation

  
• What characterizes the movement in SHM?

  Repetitive movement through an equilibrium position
• How does maximum displacement behave in SHM?

  Equal on both sides of the equilibrium
• What is the time interval of each complete vibration in SHM?

  It is the same (periodic)
• What direction does the restoring force act in SHM?

  Towards the equilibrium position
• How is the restoring force related to displacement in SHM?

  It is directly proportional to the distance
• Why is SHM considered a simple kind of oscillation?

  It is easy to analyze mathematically
• What defines an oscillation as SHM?

  Acceleration is proportional to displacement
• In SHM, what direction is the acceleration relative to displacement?

  Opposite direction to the displacement
• How does the time period of oscillation relate to amplitude in SHM?

  It is independent of the amplitude
• What is the relationship between acceleration \(a\) and displacement \(x\) in SHM?

  $a \propto -x$

  
• What is the defining equation of SHM?

  $a =$$-\omega x$
• What does the minus sign in the SHM equation indicate?

  Acceleration and displacement are opposite
• When does the bob of a pendulum reach maximum velocity?

  When it passes through the equilibrium position
• What does the graph of acceleration against displacement look like in SHM?

  A straight line through the origin sloping downwards

  
• What is the gradient of the acceleration vs. displacement graph?

  Equal to \(-\omega\)

  
• What is the SHM displacement equation?

  $x =$$A \cos(\omega t)$
• When does maximum displacement occur in the displacement equation?

  When \(\cos(\omega t)\) equals 1 or -1
• What is the displacement equation if the object starts at equilibrium?

  $x =$$A \sin(\omega t)$
• How does speed vary in SHM?

  It varies as the object oscillates
• What is the equation for speed in SHM?

  $v =$$\pm \omega \sqrt{A^2 - x^2}$
• What does the speed equation indicate about amplitude?

  Greater amplitude means greater speed
• How do you calculate angular frequency from the period?

  $\omega =$$\frac{2\pi}{T}$
• What is the displacement of a mass at time \(t = 0.3\) s if released from 4.3 cm?

  $-3.0 \text{ cm}$
• How do you calculate the speed of a pendulum at 12 cm displacement?

  Use the speed equation with given values
• What is the significance of keeping the calculator in radians mode?

  To ensure correct calculations of angles
• Why is it important to convert between time period, frequency, and angular frequency?

  Many exam questions require these conversions