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Flashcards · AP® Physics 1: Algebra-Based · Unit 7

Unit 7: Oscillations flashcards

24 cards on topics 7.1 to 7.4. Pick a topic or study the whole unit.

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7.1 Defining Simple Harmonic Motion (SHM)

What is the condition for simple harmonic motion?
The restoring force is proportional to displacement from equilibrium and opposite to it: F_net = −kx. A graph of F_net (or a) against x is a straight line through the origin with negative slope.
What is a restoring force?
A force that points towards the equilibrium position (where the net force is zero), opposite to the displacement, whichever way the object is moving.
Where is the acceleration of a simple harmonic oscillator largest and smallest?
a = −(k/m)x, so it is zero at equilibrium and largest at the turning points, x = ±A. a and x always have opposite signs.
How does gravity affect a vertical spring oscillator?
It is still SHM. Gravity only moves the equilibrium position down by d = mg/k; measure x from that new equilibrium.
Why is a pendulum only approximately in SHM?
Its restoring torque is mgℓ sin θ. For small angles (in radians) sin θ ≈ θ, so the torque is nearly proportional to θ. About 15° or less keeps the error near 1%.
Is all periodic motion simple harmonic?
No. A bouncing ball or a puck sliding between two walls repeats, but its force is not proportional to displacement, so it is not SHM.

7.2 Frequency and Period of SHM

What is the period of a mass on a spring?
T_s = 2π√(m/k). It does not depend on g, amplitude, or whether the spring is vertical or horizontal.
What is the period of a simple pendulum?
T_p = 2π√(ℓ/g), with ℓ from pivot to the centre of the bob. It does not depend on the bob's mass or (for small angles) the amplitude.
The mass on a spring is multiplied by 9. What happens to the period?
It triples, because T ∝ √m. Doubling the mass gives √2 times the period, not twice.
How do you get a straight-line graph from pendulum data?
Plot T² against ℓ: T² = (4π²/g)ℓ, so the slope is 4π²/g and g = 4π²/slope. For a spring, plot T² against m (slope 4π²/k).
How should you time an oscillation in the lab?
Time ten or more cycles and divide, starting and stopping as the object passes equilibrium. Timing one cycle lets reaction time swamp the measurement; count "zero" when starting.
How are period and frequency related?
T = 1/f, with T in s and f in Hz. A long period means a low frequency: f = 4.0 Hz gives T = 0.25 s.

7.3 Representing and Analyzing SHM

What equations give the position of an object in SHM?
Released from rest at x = +A: x = A cos(2πft). Passing equilibrium moving +x at t = 0: x = A sin(2πft). The angle is in radians.
Where are speed and acceleration zero in SHM?
At x = ±A: speed 0, acceleration largest (opposite to x). At x = 0: speed largest, acceleration 0.
Does a larger amplitude change the period of SHM?
No. Twice the amplitude gives twice the force, acceleration and top speed, so the longer path takes the same time.
How do you read the period from an x–t graph?
Measure from one peak to the next peak (or any two matching points one cycle apart). Peak to trough is only T/2.
What is the maximum acceleration of a spring–object oscillator?
a_max = kA/m, at x = ±A. In general a_x = −(k/m)x; the slope of an a–x graph is −k/m.
A 0.50 kg object on a 20 N/m spring is at x = +0.030 m. What is a_x?
a_x = −(k/m)x = −(20/0.50) × 0.030 = −1.2 m/s².

7.4 Energy of Simple Harmonic Oscillators

What is the total energy of a spring oscillator?
E = ½kA², with no friction or outside work. At any point ½mv² + ½kx² = ½kA².
Where are kinetic and potential energy largest in SHM?
At the turning points K = 0 and U is largest. At equilibrium U is smallest and K is largest. The total stays constant.
What is the maximum speed of a spring oscillator?
v_max = A√(k/m), at equilibrium. With k = 128 N/m, A = 0.050 m and m = 0.32 kg: v_max = 0.050 × √400 = 1.0 m/s.
At x = A/2 in SHM, what fraction of the energy is kinetic?
Three quarters. U = ½k(A/2)² = ¼ of ½kA², so K = ¾ of the total.
The amplitude of an oscillator doubles. How do its energy and period change?
Energy × 4 (E ∝ A²). The period is unchanged.
What is the top speed of a pendulum bob?
v_max = √(2gh_max), with h_max the release height above the lowest point. It does not depend on the bob's mass.

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