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
0.9 kgk = ?3.5 cm

Hanging a 0.9 kg mass on a spring stretches it by 3.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.9 kgx = 3.5 cmg = 9.81 m/s²
k = N/m
2.Easy
2.7 kgk = 110 N/m

A 2.7 kg mass on a spring with stiffness 110 N/m oscillates on a frictionless surface. Find the period T.

m = 2.7 kgk = 110 N/m
T = s
3.Medium
0.2 kgk = 480 N/mA = 7 cmx = 1 cm

A 0.2 kg mass on a spring with k = 480 N/m oscillates on a frictionless surface with an amplitude of 7 cm. Find its speed v when it is 1 cm from equilibrium.

m = 0.2 kgk = 480 N/mA = 7 cmx = 1 cm
v = m/s
4.Medium
L = 1.3 m

A simple pendulum has a length of 1.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.3 mg = 9.81 m/s²
T = s
5.Hard
mk = 390 N/mA = 4 cmx = 3 cm

A mass on a spring with k = 390 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 3 cm from equilibrium.

k = 390 N/mA = 4 cmx = 3 cm
U = J
6.Hard
0.9 kgk = 470 N/mA = 12 cm

A 0.9 kg mass on a spring with k = 470 N/m is pulled 12 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.9 kgk = 470 N/mA = 12 cm
vmax = m/s

Answer key

  1. 1. k = 252.3 N/m
  2. 2. T = 0.9844 s
  3. 3. v = 3.394 m/s
  4. 4. T = 2.287 s
  5. 5. U = 0.1755 J
  6. 6. vmax = 2.742 m/s

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