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7.1Oscillations

Defining Simple Harmonic Motion (SHM) — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 9 parts Lesson 2 of 10 1 quiz

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7.1 Defining Simple Harmonic Motion (SHM) — AP PHYSICS 1 notes: Describe simple harmonic motion in terms of a restoring force proportional to displacement.SHM = a special case of periodic motion in which the restoring force is proportional to the displacement from equilibrium and…

  • Equilibrium position
  • Amplitude A
  • Hooke's law
  • Newton's second law
  • Restoring torque
  • Small angles

Section 1 of 9What SHM is

What SHM is
SHM
SHM a special case of periodic motion in which the restoring force is proportional to the displacement from equilibrium and in the opposite direction, F = −kx.
Equilibrium position
  • Equilibrium position where the net force is zero, usually labelled x = 0; displacement x is measured from it.
Restoring force
  • Restoring force a force opposite to the displacement from equilibrium.
Amplitude A
  • Amplitude A maximum displacement.
Systems
  • Systems an object–ideal spring system on a frictionless surface and a pendulum with small angular displacement.

Section 2 of 9Derived equation for a spring

Hooke's law
  • Fs = −kx with k in N/m.
Newton's second law
  • Newton's second law max = −kx.
Result
  • Result the acceleration is proportional to the displacement and opposite to it.

Section 3 of 9Pendulum

Restoring torque
  • Restoring torque must be proportional to angular displacement and opposite to it.
Small angles
  • Small angles only for about 15° or less, where mg sinθ ≈ mgθ.
Large angles
  • Large angles periodic but not accurately SHM.

Section 4 of 9Features of SHM

Features of SHM
At extremes (x = ±A)
  • At extremes (x = ±A) acceleration is maximum, speed is zero.
At equilibrium
  • At equilibrium acceleration is zero, speed is maximum.
Acceleration direction
  • Acceleration direction always toward equilibrium.
Period
  • Period independent of amplitude.
Vertical spring
  • Vertical spring the new equilibrium is at kΔx0 = mg; oscillations about it are SHM with the same k.

Section 5 of 9Is it SHM?

SystemRestoring forceProportional to −x?SHM?
Mass on spring−kxYesYes, within Hooke's law
Simple pendulum−mg sinθApproximately for small θApproximately
Bouncing ballmg, constantNoNo
Floating block bobbingBuoyancy changeYesYes

Section 6 of 9Testing a motion

1
Locate the equilibrium position where the net force is zero.
2
Displace the object by x and find the net force.
3
Check whether the net force is proportional to x.
4
Check that the force points back toward equilibrium.
5
If both hold, the motion is SHM with F = −kx.

Section 7 of 9More from the specification

1Oscillation period and simple harmonic cycle
  • Oscillation period and simple harmonic cycle the time taken to complete one full mechanical oscillation cycle remains invariant across varying amplitudes.
2Frequency
  • Revolutions per second, f = 1/T.
    What the symbols mean: T = period, the time for one complete wave (s) · f = frequency (Hz)

Section 8 of 9Key terms

TermMeaning
Simple harmonic motionOscillation where restoring force is proportional to −displacement.
Restoring forceF = −kx, toward equilibrium.
Equilibrium positionPosition where the net force is zero.
AmplitudeMaximum displacement.
OscillationRepeated back-and-forth motion.

Section 9 of 9Exam technique

1
Treating any periodic motion as SHM.
2
Measuring displacement from the spring's natural length for a vertical spring instead of from the equilibrium.
3
Thinking acceleration is zero at the extremes.
4
Using a large pendulum angle and assuming SHM.

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