Circular Motion Equations Worksheet
Practice uniform circular motion with 10 problems covering centripetal acceleration, centripetal force, angular velocity, and period. Full solutions included.
View worksheet →Simple Harmonic Motion Equations Worksheet
Practice simple harmonic motion with 10 problems on period and frequency of pendulums and mass-spring systems, plus displacement, velocity, and energy in SHM.
Equations you will need
| T = 2π√(m/k) | Period of mass-spring system |
| T = 2π√(L/g) | Period of simple pendulum |
| x = A cos(ωt) | Displacement (starting at max) |
| v_max = ωA | Maximum velocity |
| a_max = ω²A | Maximum acceleration |
| E = ½kA² | Total energy in SHM |
| ω = 2π/T = 2πf | Angular frequency |
Symbol key
| Symbol | Quantity | Unit |
|---|---|---|
| T | period | s |
| f | frequency | Hz |
| m | mass | kg |
| k | spring constant | N/m |
| L | pendulum length | m |
| A | amplitude | m |
| ω | angular frequency | rad/s |
| x | displacement | m |
Practice problems
Attempt each problem on paper first, then click Show answer to check your working.
-
A 0.5 kg mass on a spring with k = 200 N/m. Find the period.
Show answer
T = 2π√(0.5/200) = 0.314 s -
Find the period of a 1.5 m pendulum. (g = 9.8 m/s²)
Show answer
T = 2π√(1.5/9.8) = 2.46 s -
A spring oscillates at 2 Hz with amplitude 0.05 m. Find max velocity.
Show answer
ω = 4π; v_max = (4π)(0.05) = 0.628 m/s -
Find the spring constant if a 2 kg mass oscillates with period 0.6 s.
Show answer
k = m(2π/T)² = 2(2π/0.6)² = 219 N/m -
A pendulum has period 2 s on Earth. Find its period on the Moon (g_M = 1.62 m/s²).
Show answer
T_M/T_E = √(g_E/g_M); T_M = 2 × √(9.8/1.62) = 4.92 s -
Mass-spring system: m = 1 kg, k = 100 N/m, A = 0.1 m. Find total energy.
Show answer
E = ½kA² = ½(100)(0.01) = 0.5 J -
Find max acceleration for a 0.05 m amplitude oscillation at 5 Hz.
Show answer
ω = 10π; a_max = (10π)²(0.05) = 49.3 m/s² -
A mass on a spring has period 0.4 s. Find ω.
Show answer
ω = 2π/0.4 = 15.7 rad/s -
A 0.2 kg mass on a spring oscillates with v_max = 1.2 m/s and A = 0.06 m. Find k.
Show answer
ω = v_max/A = 20; k = mω² = 0.2(400) = 80 N/m -
Pendulum length needed for period of exactly 1 s? (g = 9.8 m/s²)
Show answer
L = g(T/2π)² = 9.8(1/2π)² = 0.248 m
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View worksheet →About this worksheet
This simple harmonic motion equations worksheet covers the essential equations for mechanics at the A-Level / AP Physics 1 / IB HL level. Every problem has been written to mirror the style and difficulty of real exam questions, with full algebraic working shown in the solutions.
If you find these problems too straightforward, try the more advanced worksheets in the same topic listed above. If they feel too difficult, start by reviewing the equation definitions in the box at the top of this page and then return to question 1.