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
2.5 kgk = 30 N/m

A 2.5 kg mass on a spring with stiffness 30 N/m oscillates on a frictionless surface. Find the period T.

m = 2.5 kgk = 30 N/m
T = s
2.Easy
4.1 kgk = 260 N/m

A 4.1 kg mass on a spring with stiffness 260 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.1 kgk = 260 N/m
f = Hz
3.Medium
L = 1.9 m

A simple pendulum has a length of 1.9 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.9 mg = 9.81 m/s²
T = s
4.Medium
L = 0.4 m

A simple pendulum has a length of 0.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.4 mg = 9.81 m/s²
T = s
5.Hard
3.8 kgk = 320 N/mA = 9 cm

A 3.8 kg mass on a spring with k = 320 N/m is pulled 9 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.8 kgk = 320 N/mA = 9 cm
vmax = m/s
6.Hard
0.8 kgk = 190 N/mA = 7 cm

A 0.8 kg mass on a spring with k = 190 N/m is pulled 7 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.8 kgk = 190 N/mA = 7 cm
vmax = m/s

Answer key

  1. 1. T = 1.814 s
  2. 2. f = 1.267 Hz
  3. 3. T = 2.765 s
  4. 4. T = 1.269 s
  5. 5. vmax = 0.8259 m/s
  6. 6. vmax = 1.079 m/s

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