AP Physics 1 worksheet on Simple Harmonic Motion and Springs, including equations and a problem with a block-spring system.

1. The two criteria for simple harmonic motion are:
- The restoring force is directly proportional to the displacement from equilibrium.
- The restoring force acts in the direction opposite to the displacement (F = -kx).

2.
a) Period T = total time / number of oscillations = 40.0 s / 20 = 2.00 s.

b) Frequency f = 1 / T = 1 / 2.00 s = 0.500 Hz.

c) Amplitude A = distance from equilibrium (B) to extreme position (A or C). Since A to C is 40.0 cm, amplitude = 40.0 cm / 2 = 20.0 cm = 0.200 m.

d) Use T = 2π√(m/k). Solve for k:
T² = 4π²(m/k)
k = 4π²m / T² = 4π²(2 kg) / (2.00 s)² = 8π² / 4 = 2π² ≈ 19.7 N/m.

e) Position as a function of time: x(t) = A cos(ωt), where ω = 2πf = π rad/s and A = 0.200 m.
So, x(t) = 0.200 cos(π t) meters (since at t=0, mass is at maximum displacement A, cosine is appropriate).

f) Doubling the amplitude does not affect the period or frequency. Both depend only on mass and spring constant (T = 2π√(m/k)), not on amplitude. Therefore, period and frequency remain unchanged.