Essential idea:

The solution of the harmonic oscillator can be framed around the variation of kinetic and potential energy in the system.

Nature of science:

Insights: The equation for simple harmonic motion (SHM) can be solved analytically and numerically. Physicists use such solutions to help them to visualize the behavior of the oscillator. The use of the equations is very powerful as any oscillation can be described in terms of a combination of harmonic oscillators. Numerical modelling of oscillators is important in the design of electrical circuits. (1.11)

Understandings:

- The defining equation of SHM
- Energy changes

Applications and skills

- Solving problems involving acceleration, velocity and displacement during simple harmonic motion, both graphically and algebraically
- Describing the interchange of kinetic and potential energy during simple harmonic motion
- Solving problems involving energy transfer during simple harmonic motion, both graphically and algebraically

Guidance

- Contexts for this sub-topic include the simple pendulum and a mass-spring system

Data Booklet reference

*ω = 2π/T**a = -ω*^{2}x*x = x*sin_{0}*ωt*;*x = x*cos_{0}*ωt**v = ωx*cos_{0}*ωt*; v = -ωx_{0}sin*ωt**v = ±ω SQRT(x*_{0}^{2}- x^{2})*E*_{K}= 1/2 mω^{2}(x_{0}^{2}- x^{2})*E*_{T}= 1/2 mω^{2}x_{0}^{2}- pendulum:
*T = 2π SQRT(l/g)* - mass-spring:
*T = 2π SQRT(m/k)*

International-mindedness

Theory of knowledge

Utilization

Aims

**Aim 1:****Aim 2:**