Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
3.9 kgk = 300 N/m

A 3.9 kg mass on a spring with stiffness 300 N/m oscillates on a frictionless surface. Find the period T.

m = 3.9 kgk = 300 N/m
T = s
2.Easy
2.7 kgk = ?

A 2.7 kg mass on a spring oscillates with a period of 0.7 s. Find the spring stiffness k.

m = 2.7 kgT = 0.7 s
k = N/m
3.Medium
L = 0.5 m

A simple pendulum has a length of 0.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.5 mg = 9.81 m/s²
T = s
4.Medium
L = 0.9 m

A simple pendulum has a length of 0.9 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.9 mg = 9.81 m/s²
T = s
5.Hard
2.1 kgk = 50 N/mA = 8 cm

A 2.1 kg mass on a spring with k = 50 N/m is pulled 8 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.1 kgk = 50 N/mA = 8 cm
vmax = m/s
6.Hard
3.3 kgk = 50 N/mA = 9 cm

A 3.3 kg mass on a spring with k = 50 N/m is pulled 9 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.3 kgk = 50 N/mA = 9 cm
vmax = m/s

Answer key

  1. 1. T = 0.7164 s
  2. 2. k = 217.5 N/m
  3. 3. T = 1.419 s
  4. 4. T = 1.903 s
  5. 5. vmax = 0.3904 m/s
  6. 6. vmax = 0.3503 m/s

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