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
2.8 kgk = ?

A 2.8 kg mass on a spring oscillates with a period of 1.15 s. Find the spring stiffness k.

m = 2.8 kgT = 1.15 s
k = N/m
2.Easy
3.9 kgk = 110 N/m

A 3.9 kg mass on a spring with stiffness 110 N/m oscillates on a frictionless surface. Find the period T.

m = 3.9 kgk = 110 N/m
T = s
3.Medium
L = 2 m

A simple pendulum has a length of 2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2 mg = 9.81 m/s²
T = s
4.Medium
L = 0.8 mT = 2.91 s

An astronaut on another planet finds that a simple pendulum 0.8 m long has a period of 2.91 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.8 mT = 2.91 s
g = m/s²
5.Hard
2.5 kgk = 160 N/mA = 20 cm

A 2.5 kg mass on a spring with k = 160 N/m is pulled 20 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.5 kgk = 160 N/mA = 20 cm
vmax = m/s
6.Hard
2.6 kgk = 380 N/mA = 13 cm

A 2.6 kg mass on a spring with k = 380 N/m is pulled 13 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.6 kgk = 380 N/mA = 13 cm
amax = m/s²

Answer key

  1. 1. k = 83.58 N/m
  2. 2. T = 1.183 s
  3. 3. T = 2.837 s
  4. 4. g = 3.73 m/s²
  5. 5. vmax = 1.6 m/s
  6. 6. amax = 19 m/s²

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