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
2.9 kgk = 230 N/m

A 2.9 kg mass on a spring with stiffness 230 N/m oscillates on a frictionless surface. Find the period T.

m = 2.9 kgk = 230 N/m
T = s
2.Easy
1.7 kgk9 cm

Hanging a 1.7 kg mass on a spring stretches it by 9 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 1.7 kgx = 9 cmg = 9.81 m/s²
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.9 s? Use g = 9.81 m/s². Find L.

T = 1.9 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.5 s? Use g = 9.81 m/s². Find L.

T = 1.5 sg = 9.81 m/s²
L = m
5.Hard
1 kgk = 350 N/mA = 20 cm

A 1 kg mass on a spring with k = 350 N/m is pulled 20 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1 kgk = 350 N/mA = 20 cm
amax = m/s²
6.Hard
2.9 kgk = 420 N/mA = 17 cm

A 2.9 kg mass on a spring with k = 420 N/m is pulled 17 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.9 kgk = 420 N/mA = 17 cm
amax = m/s²

Answer key

  1. 1. T = 0.7055 s
  2. 2. T = 0.6018 s
  3. 3. L = 0.897 m
  4. 4. L = 0.5591 m
  5. 5. amax = 70 m/s²
  6. 6. amax = 24.62 m/s²

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