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
0.5 kgk22 cm

Hanging a 0.5 kg mass on a spring stretches it by 22 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 = 0.5 kgx = 22 cmg = 9.81 m/s²
T = s
2.Easy
2.1 kgk = 140 N/m

A 2.1 kg mass on a spring with stiffness 140 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.1 kgk = 140 N/m
f = Hz
3.Medium
L = 0.3 m

A simple pendulum has a length of 0.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.3 mg = 9.81 m/s²
T = s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.2 s? Use g = 9.81 m/s². Find L.

T = 1.2 sg = 9.81 m/s²
L = m
5.Hard
mk = 70 N/mA = 10 cmx = 4 cm

A mass on a spring with k = 70 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find the energy U stored in the spring when the mass is 4 cm from equilibrium.

k = 70 N/mA = 10 cmx = 4 cm
U = J
6.Hard
2.4 kgk = 330 N/mA = 12 cm

A 2.4 kg mass on a spring with k = 330 N/m is pulled 12 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.4 kgk = 330 N/mA = 12 cm
vmax = m/s

Answer key

  1. 1. T = 0.9409 s
  2. 2. f = 1.299 Hz
  3. 3. T = 1.099 s
  4. 4. L = 0.3578 m
  5. 5. U = 0.056 J
  6. 6. vmax = 1.407 m/s

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