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
1.4 kgk20 cm

Hanging a 1.4 kg mass on a spring stretches it by 20 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 = 1.4 kgx = 20 cmg = 9.81 m/s²
T = s
2.Easy
2 kgk = 270 N/m

A 2 kg mass on a spring with stiffness 270 N/m oscillates on a frictionless surface. Find the period T.

m = 2 kgk = 270 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.6 s? Use g = 9.81 m/s². Find L.

T = 1.6 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1 s? Use g = 9.81 m/s². Find L.

T = 1 sg = 9.81 m/s²
L = m
5.Hard
mk = 180 N/mA = 4 cmx = 2 cm

A mass on a spring with k = 180 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 2 cm from equilibrium.

k = 180 N/mA = 4 cmx = 2 cm
U = J
6.Hard
0.6 kgk = 480 N/mA = 7 cm

A 0.6 kg mass on a spring with k = 480 N/m is pulled 7 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.6 kgk = 480 N/mA = 7 cm
amax = m/s²

Answer key

  1. 1. T = 0.8971 s
  2. 2. T = 0.5408 s
  3. 3. L = 0.6361 m
  4. 4. L = 0.2485 m
  5. 5. U = 0.036 J
  6. 6. amax = 56 m/s²

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