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Maximum speed in simple harmonic motion calculator

A-level Oscillations

The greatest speed of an object in simple harmonic motion, reached at the equilibrium position.

v_max = 2πf x₀

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

v_maxMaximum speed to find 0.628 m/s

fFrequency

x₀Amplitude

Significant figures

Working

Write the equation
v_max = 2πf x₀
Substitute the values
v_max = 2π × 2 × 0.05
Calculate
v_max = 0.628319 m/s
Give the answer to 3 significant figures
v_max = 0.628 m/s

Worked example

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

Write the equation
v_max = 2πf x₀
Substitute the values
v_max = 2π × 2 × 0.05
Calculate
v_max = 0.628319 m/s
Give the answer to 3 significant figures
v_max = 0.628 m/s

Symbols and units

Symbol	Quantity	SI unit
v_max	Maximum speed	m/s
f	Frequency	Hz
x₀	Amplitude	m

Maximum speed in simple harmonic motion: rearranged

To find maximum speed: v_max = 2πf x₀
To find frequency: f = v_max / (2πx₀)
To find amplitude: x₀ = v_max / (2πf)

Exam tip

Equivalent to ωx₀. The speed is zero at the ends of the motion.

Common questions

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

The equation is vmax = 2πf x0, where vmax is the maximum speed (m/s); f is the frequency (Hz); x0 is the amplitude (m).

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

In SI units: maximum speed in m/s, 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 vmax = 2πf x0?

Rearranging gives these forms: to find maximum speed: vmax = 2πf x0. to find frequency: f = vmax / (2πx0). to find amplitude: x0 = vmax / (2πf).

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More oscillations equations: Time period of a mass on a spring, Time period of a simple pendulum, Maximum acceleration in simple harmonic motion. See the full list on the a-level physics equation calculator page.