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
4.9 kgk = 170 N/m

A 4.9 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the period T.

m = 4.9 kgk = 170 N/m
T = s
2.Easy
1.9 kgk = 400 N/m

A 1.9 kg mass on a spring with stiffness 400 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.9 kgk = 400 N/m
f = Hz
3.Medium
L = 2.3 m

A simple pendulum has a length of 2.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.3 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
2.9 kgk = 240 N/mA = 10 cm

A 2.9 kg mass on a spring with k = 240 N/m is pulled 10 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.9 kgk = 240 N/mA = 10 cm
E = J
6.Hard
2 kgk = 220 N/mA = 20 cm

A 2 kg mass on a spring with k = 220 N/m is pulled 20 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2 kgk = 220 N/mA = 20 cm
amax = m/s²

Answer key

  1. 1. T = 1.067 s
  2. 2. f = 2.309 Hz
  3. 3. T = 3.042 s
  4. 4. T = 1.903 s
  5. 5. E = 1.2 J
  6. 6. amax = 22 m/s²

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