Master Simple Harmonic Motion with AP Physics 1 review games.
This unit covers springs, pendulums, oscillation period and restoring force — essential concepts for AP Physics 1. Use our interactive study games to test your understanding, or review questions in traditional format below.
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This unit covers springs, pendulums, oscillation period and restoring force — essential concepts for AP Physics 1. Use our interactive study games to test your understanding, or review questions in traditional format below.
Key Concepts Breakdown
1 Springs
Students must understand Hooke's Law (F = -kx) and how spring constant k relates to stiffness. The elastic potential energy stored in a spring is PE = ½kx², and energy conservation governs the exchange between kinetic and potential energy in a spring-mass system. Know how combining springs in series vs. parallel affects the effective spring constant.
Key Points
- Hooke's Law: F = -kx; negative sign indicates restoring force opposes displacement
- Elastic PE = ½kx²; max KE occurs at equilibrium (x = 0), max PE at amplitude (x = A)
- Springs in parallel: k_eff = k₁ + k₂; springs in series: 1/k_eff = 1/k₁ + 1/k₂
- Period of spring-mass system: T = 2π√(m/k); independent of amplitude and gravitational field
A 0.5 kg block is attached to a spring with k = 200 N/m and displaced 0.1 m from equilibrium. What is the maximum speed of the block?
Use energy conservation: ½kA² = ½mv²_max, so v_max = A√(k/m). Substituting: v_max = (0.1)√(200/0.5) = (0.1)(20) = 2.0 m/s. Maximum speed always occurs at the equilibrium position where all potential energy has converted to kinetic energy.
2 Pendulums
A simple pendulum undergoes SHM only for small angles (θ < ~15°), where the restoring force is approximately F = -mg sinθ ≈ -mgθ. The period depends only on length and gravitational field strength, not on mass or amplitude. Students must be able to compare pendulum behavior on different planets or with different string lengths.
Key Points
- Period: T = 2π√(L/g); depends on length L and gravitational field g only
- Mass of the bob does NOT affect the period
- Amplitude does NOT affect the period (small-angle approximation)
- Restoring force is the tangential component of gravity: F = -mg sinθ ≈ -mgθ for small θ
A pendulum has a period of 2.0 s on Earth (g = 10 m/s²). What is its period on a planet where g = 2.5 m/s²?
From T = 2π√(L/g), the length L is fixed, so T ∝ 1/√g. Taking the ratio: T_planet/T_Earth = √(g_Earth/g_planet) = √(10/2.5) = √4 = 2. Therefore T_planet = 2 × 2.0 s = 4.0 s. Decreasing g weakens the restoring force, slowing the oscillation.
3 Oscillation Period
Period (T) is the time for one complete oscillation; frequency (f) is oscillations per second; they are related by T = 1/f. For the AP exam, students must know the period formulas for both springs and pendulums and understand which physical variables affect each. Angular frequency ω = 2πf = 2π/T appears in graphs and equations of motion.
Key Points
- T = 1/f and f = 1/T; SI units: T in seconds, f in hertz (Hz)
- Spring-mass: T = 2π√(m/k) — increases with more mass, decreases with stiffer spring
- Pendulum: T = 2π√(L/g) — increases with longer string, decreases with stronger gravity
- Neither period formula depends on amplitude (a key AP exam distinction)
A student doubles the mass on a spring and also doubles the spring constant. How does the period change?
Using T = 2π√(m/k), the new period is T' = 2π√(2m/2k) = 2π√(m/k) = T. Because both m and k doubled by the same factor, the ratio m/k is unchanged, so the period remains the same. This type of proportional reasoning question is common on the AP exam.
4 Restoring Force
The restoring force is the net force directed back toward equilibrium that causes oscillatory motion; it must be proportional to displacement for true SHM (F = -kx). At maximum displacement (amplitude), the restoring force and acceleration are maximum; at equilibrium, both are zero while velocity is maximum. Understanding force and acceleration direction relative to displacement is critical for free-response questions.
Key Points
- Restoring force always points toward equilibrium, opposite to displacement
- At x = A (amplitude): |F| and |a| are maximum, v = 0
- At x = 0 (equilibrium): F = 0, a = 0, |v| is maximum
- Acceleration is NOT constant — use F = ma with F = -kx, giving a = -(k/m)x
A 2 kg block on a spring (k = 50 N/m) is at x = +0.4 m from equilibrium. Find the magnitude and direction of the net force and the acceleration.
The restoring force is F = -kx = -(50)(0.4) = -20 N; the negative sign means it points in the negative x-direction (toward equilibrium). The acceleration is a = F/m = -20/2 = -10 m/s², also directed toward equilibrium. Because the object is displaced in the positive direction, both the force and acceleration point in the negative direction.
Questions, answered.
What is Simple Harmonic Motion?
Simple Harmonic Motion is Unit 6 of AP Physics 1, covering springs, pendulums, oscillation period and restoring force.
How to study for AP Physics 1 Unit 6?
Start with the Quick Summary above, review the Key Concepts, then test yourself with our interactive study games. Aim for 80%+ accuracy before moving on.
How many questions are in this unit?
This unit has 28+ review questions across 5 different game modes.