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
3.3 kgk = ?

A 3.3 kg mass on a spring oscillates with a period of 2.05 s. Find the spring stiffness k.

m = 3.3 kgT = 2.05 s
k = N/m
2.Easy
0.4 kgk = ?24 cm

Hanging a 0.4 kg mass on a spring stretches it by 24 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.4 kgx = 24 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 1.6 mT = 4.12 s

An astronaut on another planet finds that a simple pendulum 1.6 m long has a period of 4.12 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.6 mT = 4.12 s
g = m/s²
4.Medium
3.1 kgk = 380 N/mA = 4 cmx = 2 cm

A 3.1 kg mass on a spring with k = 380 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find its speed v when it is 2 cm from equilibrium.

m = 3.1 kgk = 380 N/mA = 4 cmx = 2 cm
v = m/s
5.Hard
1.1 kgk = 260 N/mA = 3 cm

A 1.1 kg mass on a spring with k = 260 N/m is pulled 3 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.1 kgk = 260 N/mA = 3 cm
amax = m/s²
6.Hard
2.4 kgk = 270 N/mA = 15 cm

A 2.4 kg mass on a spring with k = 270 N/m is pulled 15 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.4 kgk = 270 N/mA = 15 cm
vmax = m/s

Answer key

  1. 1. k = 31 N/m
  2. 2. k = 16.35 N/m
  3. 3. g = 3.721 m/s²
  4. 4. v = 0.3835 m/s
  5. 5. amax = 7.091 m/s²
  6. 6. vmax = 1.591 m/s

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