Mechanics
Mass on a spring
Watch the mass bob up and down in simple harmonic motion.
Study simple harmonic motion with a mass on a spring. Measure period, angular frequency, and energy oscillation with adjustable mass and spring constant.
Spring oscillation
A mass on a spring oscillates because the spring exerts a restoring force proportional to displacement (Hooke’s law).
When stretched or compressed, the spring pulls the mass back toward equilibrium. Energy swaps between spring potential energy and kinetic energy, producing simple harmonic motion.
- F = −kx
- T ≈ 2π√(m/k)
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
If you double the mass hanging on the spring, does the oscillation period double?
Predictions to weigh
- The period doubles.
- The period stays the same.
- The period increases, but by less than double.
Variable roles
What you set:
- Mass (kg)
- Spring constant (N/m)
What you measure:
- Period (s)
- Equilibrium extension (m)
How the investigation runs
- Open the Mass-on-Spring preset in the Mechanics module. A ball (the bob) hangs from a spring anchored above it.
- Note the speed probe already attached to the bob — it reports the bob's instantaneous speed as it oscillates.
- For each row, set the bob's mass and the spring's stiffness, pull the bob down slightly, release it, and let it oscillate and settle.
Governing equation
Spring Period (SHM) — T = 2π·√(m / k)
For a mass oscillating on an ideal spring, the period depends only on the mass and the spring constant — not on amplitude or on gravity.
Kinetic Energy at Equilibrium — KE = ½·m·v²
The bob's speed is greatest as it passes through the equilibrium point; read that peak speed off the probe to find its kinetic energy there.
What the printable worksheet asks students to work out
- Using T = 2π√(m/k), calculate the period for each row and compare it to the value you timed in the sandbox.
- Rows 1 and 3 have masses in a 1:4 ratio. By what factor did the period change? Does that match √4 = 2?
Where this shows up beyond the lab
- If you increased the spring constant k instead of the mass, would the period increase or decrease? Sketch the trend you'd expect.
- The bob visibly hangs lower under gravity (equilibrium extension = mg/k), yet gravity g does not appear in T = 2π√(m/k). Explain why the period is unaffected by gravity even though the equilibrium position is.
- AP Physics 1 — Unit 7: Oscillations
- AP Physics C: Mechanics — Unit 7: Oscillations
- IB Physics — A.1 Kinematics
- IB Physics — C.1 Simple harmonic motion
- General High School Physics — Waves & sound
- NGSS High School Physics — Energy accounting in systems
- Middle School Physical Science — Stored (potential) energy
- Welcome to Mass On Spring
- Select the bob
- Press Play
- Up and down
- Open the data
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.