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
2.3 kgk = ?2 cm

Hanging a 2.3 kg mass on a spring stretches it by 2 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.3 kgx = 2 cmg = 9.81 m/s²
k = N/m
2.Easy
0.6 kgk23 cm

Hanging a 0.6 kg mass on a spring stretches it by 23 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 = 0.6 kgx = 23 cmg = 9.81 m/s²
T = s
3.Medium
1.7 kgk = 60 N/mA = 10 cmx = 6 cm

A 1.7 kg mass on a spring with k = 60 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find its speed v when it is 6 cm from equilibrium.

m = 1.7 kgk = 60 N/mA = 10 cmx = 6 cm
v = m/s
4.Medium
L = 1.3 mT = 1.44 s

An astronaut on another planet finds that a simple pendulum 1.3 m long has a period of 1.44 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.3 mT = 1.44 s
g = m/s²
5.Hard
3.8 kgk = 50 N/mA = 8 cm

A 3.8 kg mass on a spring with k = 50 N/m is pulled 8 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.8 kgk = 50 N/mA = 8 cm
vmax = m/s
6.Hard
3.1 kgk = 190 N/mA = 17 cm

A 3.1 kg mass on a spring with k = 190 N/m is pulled 17 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.1 kgk = 190 N/mA = 17 cm
amax = m/s²

Answer key

  1. 1. k = 1128 N/m
  2. 2. T = 0.9621 s
  3. 3. v = 0.4753 m/s
  4. 4. g = 24.75 m/s²
  5. 5. vmax = 0.2902 m/s
  6. 6. amax = 10.42 m/s²

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