Title: InkPhysics / Periodic motion
On every note of this deck, unless a note says otherwise:
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Front: RECALL
State the condition for a simple pendulum to move with SHM.
Back: The amplitude of the swings must be small.

Front: SPOT THE ERROR
Say what is wrong with this claim: Bigger swings take longer.
Back: In SHM the period is independent of amplitude. A larger swing travels further, but the restoring force and speed grow in proportion, so the period stays the same.

Front: RECALL
State the frequency of the energy variation in SHM.
Back: Kinetic and potential energy each vary at twice the frequency of the oscillation.

Front: RECALL
State the energy transfer at resonance.
Back: At resonance, energy is transferred from the driver to the oscillating system at the maximum rate.

Front: DEFINITION
Define: Natural frequency.
Back: The frequency at which a system oscillates freely after a single displacement, with no driving force.

Front: RECALL
State the effect of light damping on the period.
Back: Almost none: the amplitude decays but the period is nearly unchanged.

Front: RECALL
State where the speed in SHM is greatest.
Back: At the equilibrium position, where the displacement is zero.

Front: DEFINITION
Define: Resonance.
Back: The large-amplitude oscillation of a system when the driving frequency equals its natural frequency. That is the lightly damped case; heavier damping moves the peak slightly below the natural frequency.

Front: RECALL
State the phase of velocity relative to displacement in SHM.
Back: Velocity leads displacement by a quarter of a cycle (90°).

Front: RECALL
State what provides the centripetal force.
Back: A real named force such as tension, gravity, friction or a normal reaction, never a new force of its own.

Front: SPOT THE ERROR
Say what is wrong with this claim: Pushing harder is all that matters.
Back: Driving frequency decides the magnification, not the size of the response on its own. Double the driving force at any frequency and you double the amplitude; what matching the natural frequency buys you is the factor by which that push is magnified, which is why a small push at the right frequency beats a large one at the wrong one.

Front: SPOT THE ERROR
Say what is wrong with this claim: You're flung outwards by centrifugal force.
Back: There is no outward centrifugal force. Your inertia carries you straight on while the car turns; the resultant of the real forces acts towards the centre of the circle.

Front: DEFINITION
Define: Damping.
Back: The loss of energy from an oscillating system to resistive forces, reducing the amplitude over time.

Front: RECALL
State the path of an object when the centripetal force is removed.
Back: A straight line along the tangent to the circle, by Newton's first law.

Front: RECALL
State the total energy of a simple harmonic oscillator.
Back: For a mass-spring system E = ½kA^2; equivalently, for any simple harmonic oscillator, E = ½mω^2x_0^2, where x_0 is the amplitude. The two are the same expression, since ω^2 = k/m.

Front: RECALL
State the phase lag of a driven oscillator at its natural frequency.
Back: The oscillator lags the driver by a quarter of a cycle (90°), and by exactly that whatever the damping. The amplitude peak can sit a little below the natural frequency; the quarter-cycle lag does not move.

Front: RECALL
State where the acceleration in SHM is greatest.
Back: At the extremes of the motion, where the displacement is at a maximum.

Front: DEFINITION
Define: Simple harmonic motion.
Back: Oscillation in which the acceleration is proportional to the displacement from equilibrium and directed towards it: a = −ω^2x.

Front: RECALL
State how the centripetal acceleration formula is derived from a vector diagram.
Back: Two velocities an angle Δθ apart have equal length but differ in direction. Drawn from a common tail their difference is Δv = vΔθ, pointing along the inward radius at the middle of the arc; dividing by Δt = Δθ/ω gives a = vω, and then v = ωr gives v^2/r = ω^2r.

Front: RECALL
State the frequency of forced vibrations.
Back: A driven system oscillates at the driving frequency, not at its natural frequency.

Front: RECALL
Explain how plastic deformation reduces the amplitude of an oscillation.
Back: A ductile part taken past its yield point on each swing keeps a permanent set, so the work done deforming it is not returned to the oscillation but goes to moving dislocations and warming the metal. Energy leaves the system every cycle, so the amplitude falls.

Front: RECALL
State the direction of the centripetal acceleration.
Back: Towards the centre of the circle, at right angles to the velocity.

Front: SPOT THE ERROR
Say what is wrong with this claim: Heavier pendulums swing slower.
Back: A pendulum's period is independent of mass: T = 2π√(L/g) depends only on length and g. Mass appears in the period only for a mass on a spring.

Front: RECALL
State the effect of increased damping on the resonance curve.
Back: The amplitude peak becomes lower and broader, and moves to a slightly lower frequency.

Front: DEFINITION
Define: Angular speed.
Back: The angle swept out per unit time: ω = θ/t = 2πf, in rad s^−1.

Front: DEFINITION
Define: The radian.
Back: The angle subtended at the centre of a circle by an arc equal in length to the radius.