IB DP Physics: HL复习笔记9.1.3 Calculating Energy Changes in SHM

• There are many equations to learn in the topic of simple harmonic motion
• The key equations are summarised below:

A summary of the equations related to simple harmonic motion. The green stars indicate equations which are not included in the IB data booklet

Part (a)

Step 1: List the known quantities

• • • Mass of the particle, m = 45 g = 45 × 10−3 kg

Step 2: Use the graph to determine the maximum potential energy of the particle

• • • Maximum potential energy, EPmax = 60 mJ = 60 × 10−3 J

Step 3: Determine the amplitude of the oscillation

• • • The amplitude of the motion, x0, is the maximum displacement
    • At the maximum displacement, the particle is at its highest point, hence this is the position of maximum potential energy
    • From the graph, when EP = EPmax:

x02 = 8.0 cm = 0.08 m

• • • Therefore, the amplitude is:

x0 = √0.08 = 0.28 m

Step 4: Write down the equation for the potential energy of an oscillator

Part (b)

Step 1: List the known quantities

• • • Angular velocity, ω = 5.77 rad s−1
    • Amplitude, x0 = 0.28 m

Step 2: Write down the equation for the maximum speed of an oscillator

vmax = ωx0

Step 3: Substitute in the known quantities

vmax = 5.77 × 0.28 = 1.6 m s−1

Part (a)

Step 1: Read the values of amplitude and time period from the graph

Step 2: State the values of amplitude and time period

• • • Amplitude, x0 = 0.3 m
    • Time period, T = 2.0 s

Part (b)

Step 1: List the known quantities

• • • Mass of the oscillator, m = 200 g = 0.2 kg

Step 2: Write down the equation for the maximum speed of an oscillator

vmax = ωx0

Step 3: Write down the equation relating angular speed and time period

Step 1: Write down all known quantities

• • Mass, m = 23 g = 23 × 10–3 kg
  • Amplitude, x0 = 1.5 cm = 0.015 m
  • Frequency, f = 4.8 Hz

Step 2: Write down the equation for the total energy of SHM oscillations: