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
1 kgk = 300 N/m

A 1 kg mass on a spring with stiffness 300 N/m oscillates on a frictionless surface. Find the period T.

m = 1 kgk = 300 N/m
T = s
2.Easy
1.1 kgk = 130 N/m

A 1.1 kg mass on a spring with stiffness 130 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.1 kgk = 130 N/m
f = Hz
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 = 2.6 m

A simple pendulum has a length of 2.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.6 mg = 9.81 m/s²
T = s
5.Hard
mk = 490 N/mA = 8 cmx = 2 cm

A mass on a spring with k = 490 N/m oscillates on a frictionless surface with an amplitude of 8 cm. Find the energy U stored in the spring when the mass is 2 cm from equilibrium.

k = 490 N/mA = 8 cmx = 2 cm
U = J
6.Hard
mk = 150 N/mA = 4 cmx = 1 cm

A mass on a spring with k = 150 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find the energy U stored in the spring when the mass is 1 cm from equilibrium.

k = 150 N/mA = 4 cmx = 1 cm
U = J

Answer key

  1. 1. T = 0.3628 s
  2. 2. f = 1.73 Hz
  3. 3. T = 1.419 s
  4. 4. T = 3.235 s
  5. 5. U = 0.098 J
  6. 6. U = 0.0075 J

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