Maximum acceleration in simple harmonic motion calculator

Worked example

Find amax, the maximum acceleration. Given: frequency f = 2.00 Hz; amplitude x0 = 0.0500 m.

1. Write the equation
   a_max = 4π² f² x₀
2. Substitute the values
   a_max = 4π² × 2² × 0.05
3. Calculate
   a_max = 7.89568 m/s²
4. Give the answer to 3 significant figures
   a_max = 7.90 m/s²

Symbols and units

Maximum acceleration in simple harmonic motion: rearranged

• To find maximum acceleration: a_max = 4π² f² x₀
• To find frequency: f = √(a_max / (4π² x₀))
• To find amplitude: x₀ = a_max / (4π² f²)

Exam tip

Equivalent to ω²x₀. The acceleration is zero at the equilibrium position.

Common questions

What is the formula for maximum acceleration in simple harmonic motion?

The equation is amax = 4π² f² x0, where amax is the maximum acceleration (m/s²); f is the frequency (Hz); x0 is the amplitude (m).

What units should I use for maximum acceleration in simple harmonic motion?

In SI units: maximum acceleration in m/s², frequency in Hz, amplitude in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange amax = 4π² f² x0?

Rearranging gives these forms: to find maximum acceleration: amax = 4π² f² x0. to find frequency: f = √(amax / (4π² x0)). to find amplitude: x0 = amax / (4π² f²).