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
2.6 kgk = ?

A 2.6 kg mass on a spring makes 30 complete oscillations in 51 s. Find the spring stiffness k.

m = 2.6 kgN = 30t = 51 s
k = N/m
2.Easy
1.9 kgk = ?4 cm

Hanging a 1.9 kg mass on a spring stretches it by 4 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.9 kgx = 4 cmg = 9.81 m/s²
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 0.8 s? Use g = 9.81 m/s². Find L.

T = 0.8 sg = 9.81 m/s²
L = m
4.Medium
L = 2 mT = 2.66 s

An astronaut on another planet finds that a simple pendulum 2 m long has a period of 2.66 s for small swings. Find the gravitational acceleration g on that planet.

L = 2 mT = 2.66 s
g = m/s²
5.Hard
0.6 kgk = 430 N/mA = 4 cm

A 0.6 kg mass on a spring with k = 430 N/m is pulled 4 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.6 kgk = 430 N/mA = 4 cm
vmax = m/s
6.Hard
3.3 kgk = 350 N/mA = 2 cm

A 3.3 kg mass on a spring with k = 350 N/m is pulled 2 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.3 kgk = 350 N/mA = 2 cm
vmax = m/s

Answer key

  1. 1. k = 35.52 N/m
  2. 2. k = 466 N/m
  3. 3. L = 0.159 m
  4. 4. g = 11.16 m/s²
  5. 5. vmax = 1.071 m/s
  6. 6. vmax = 0.206 m/s

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