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 kgk = ?

A 1 kg mass on a spring oscillates with a period of 0.7 s. Find the spring stiffness k.

m = 1 kgT = 0.7 s
k = N/m
2.Easy
2.8 kgk = 50 N/m

A 2.8 kg mass on a spring with stiffness 50 N/m oscillates on a frictionless surface. Find the period T.

m = 2.8 kgk = 50 N/m
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 = 1.5 mT = 4 s

An astronaut on another planet finds that a simple pendulum 1.5 m long has a period of 4 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.5 mT = 4 s
g = m/s²
5.Hard
1 kgk = 440 N/mA = 12 cm

A 1 kg mass on a spring with k = 440 N/m is pulled 12 cm from equilibrium and released. Find its maximum speed vmax.

m = 1 kgk = 440 N/mA = 12 cm
vmax = m/s
6.Hard
1.4 kgk = 150 N/mA = 18 cm

A 1.4 kg mass on a spring with k = 150 N/m is pulled 18 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.4 kgk = 150 N/mA = 18 cm
amax = m/s²

Answer key

  1. 1. k = 80.57 N/m
  2. 2. T = 1.487 s
  3. 3. L = 1.203 m
  4. 4. g = 3.701 m/s²
  5. 5. vmax = 2.517 m/s
  6. 6. amax = 19.29 m/s²

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