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
1.3 kgk = 80 N/m

A 1.3 kg mass on a spring with stiffness 80 N/m oscillates on a frictionless surface. Find the period T.

m = 1.3 kgk = 80 N/m
T = s
2.Easy
1.6 kgk = 110 N/m

A 1.6 kg mass on a spring with stiffness 110 N/m oscillates on a frictionless surface. Find the period T.

m = 1.6 kgk = 110 N/m
T = s
3.Medium
L = 1.1 m

A simple pendulum has a length of 1.1 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.1 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.7 s? Use g = 9.81 m/s². Find L.

T = 1.7 sg = 9.81 m/s²
L = m
5.Hard
mk = 210 N/mA = 17 cmx = 3 cm

A mass on a spring with k = 210 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find the energy U stored in the spring when the mass is 3 cm from equilibrium.

k = 210 N/mA = 17 cmx = 3 cm
U = J
6.Hard
2.3 kgk = 330 N/mA = 6 cm

A 2.3 kg mass on a spring with k = 330 N/m is pulled 6 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.3 kgk = 330 N/mA = 6 cm
vmax = m/s

Answer key

  1. 1. T = 0.801 s
  2. 2. T = 0.7578 s
  3. 3. T = 2.104 s
  4. 4. L = 0.7181 m
  5. 5. U = 0.0945 J
  6. 6. vmax = 0.7187 m/s

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