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
0.3 kgk1 cm

Hanging a 0.3 kg mass on a spring stretches it by 1 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 = 0.3 kgx = 1 cmg = 9.81 m/s²
T = s
2.Easy
4.8 kgk = 110 N/m

A 4.8 kg mass on a spring with stiffness 110 N/m oscillates on a frictionless surface. Find the period T.

m = 4.8 kgk = 110 N/m
T = s
3.Medium
3.7 kgk = 310 N/mA = 18 cmx = 6 cm

A 3.7 kg mass on a spring with k = 310 N/m oscillates on a frictionless surface with an amplitude of 18 cm. Find its speed v when it is 6 cm from equilibrium.

m = 3.7 kgk = 310 N/mA = 18 cmx = 6 cm
v = m/s
4.Medium
L = 1.6 m

A simple pendulum has a length of 1.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.6 mg = 9.81 m/s²
T = s
5.Hard
mk = 360 N/mA = 15 cmx = 3 cm

A mass on a spring with k = 360 N/m oscillates on a frictionless surface with an amplitude of 15 cm. Find its kinetic energy K when it is 3 cm from equilibrium.

k = 360 N/mA = 15 cmx = 3 cm
K = J
6.Hard
0.7 kgk = 100 N/mA = 5 cm

A 0.7 kg mass on a spring with k = 100 N/m is pulled 5 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.7 kgk = 100 N/mA = 5 cm
amax = m/s²

Answer key

  1. 1. T = 0.2006 s
  2. 2. T = 1.313 s
  3. 3. v = 1.553 m/s
  4. 4. T = 2.537 s
  5. 5. K = 3.888 J
  6. 6. amax = 7.143 m/s²

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