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
3 kgk = 280 N/m

A 3 kg mass on a spring with stiffness 280 N/m oscillates on a frictionless surface. Find the period T.

m = 3 kgk = 280 N/m
T = s
2.Easy
0.7 kgk19 cm

Hanging a 0.7 kg mass on a spring stretches it by 19 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 = 0.7 kgx = 19 cmg = 9.81 m/s²
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.2 s? Use g = 9.81 m/s². Find L.

T = 2.2 sg = 9.81 m/s²
L = m
4.Medium
L = 2 m

A simple pendulum has a length of 2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2 mg = 9.81 m/s²
T = s
5.Hard
mk = 290 N/mA = 7 cmx = 3 cm

A mass on a spring with k = 290 N/m oscillates on a frictionless surface with an amplitude of 7 cm. Find the energy U stored in the spring when the mass is 3 cm from equilibrium.

k = 290 N/mA = 7 cmx = 3 cm
U = J
6.Hard
1.1 kgk = 20 N/mA = 4 cm

A 1.1 kg mass on a spring with k = 20 N/m is pulled 4 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.1 kgk = 20 N/mA = 4 cm
vmax = m/s

Answer key

  1. 1. T = 0.6504 s
  2. 2. T = 0.8744 s
  3. 3. L = 1.203 m
  4. 4. T = 2.837 s
  5. 5. U = 0.1305 J
  6. 6. vmax = 0.1706 m/s

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