SHM Explorer
Drag a mass on a spring or a pendulum bob, release it and follow displacement, velocity, acceleration and energy on linked graphs, with light, critical and heavy damping.
Learning goals
- Use oscillation quantities and describe free oscillations and their investigation.
- Relate displacement, velocity, acceleration and phase in simple harmonic motion.
- Identify and analyse simple harmonic motion using its defining equation and sinusoidal solutions.
- Describe kinetic–potential energy interchange in ideal simple harmonic motion.
A 0.50 kilogram mass on a spring of constant 20 newtons per metre, displaced 0.15 metres with no damping. Not released yet.
- Period, T
- 0.993 s
- ω = 2π/T
- 6.32 rad/s
- Displacement, x
- 0.150 m
- Velocity, v
- 0.000 m/s
- Acceleration, a
- −6.00 m/s²
- Maximum speed
- — m/s
Try this
0 of 4 donePause the motion when the acceleration is greatest. (not done yet)
The acceleration is greatest at the extremes, where the velocity is zero, and it points back towards equilibrium.
Pause the motion as the mass passes through the equilibrium position. (not done yet)
At x = 0 the acceleration is zero and the speed is greatest: vmax = ωx₀.
Release the same oscillator from two amplitudes, one at least twice the other. (not done yet)
The period stays the same: T = 2π/ω does not depend on amplitude. A pendulum keeps this only for small angles.
Release it with light, critical and heavy damping. Which returns to equilibrium fastest? (not done yet)
Critical damping returns it fastest without overshooting; heavy damping creeps back and light damping overshoots. Car suspensions are designed to be close to critical.