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
0.2 kgk = ?10 cm

Hanging a 0.2 kg mass on a spring stretches it by 10 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.2 kgx = 10 cmg = 9.81 m/s²
k = N/m
2.Easy
1.6 kgk = ?

A 1.6 kg mass on a spring makes 15 complete oscillations in 43 s. Find the spring stiffness k.

m = 1.6 kgN = 15t = 43 s
k = N/m
3.Medium
L = 0.3 m

A simple pendulum has a length of 0.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.3 mg = 9.81 m/s²
T = s
4.Medium
L = 3 m

A simple pendulum has a length of 3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 3 mg = 9.81 m/s²
T = s
5.Hard
1.3 kgk = 180 N/mA = 3 cm

A 1.3 kg mass on a spring with k = 180 N/m is pulled 3 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.3 kgk = 180 N/mA = 3 cm
amax = m/s²
6.Hard
3.6 kgk = 500 N/mA = 17 cm

A 3.6 kg mass on a spring with k = 500 N/m is pulled 17 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.6 kgk = 500 N/mA = 17 cm
amax = m/s²

Answer key

  1. 1. k = 19.62 N/m
  2. 2. k = 7.686 N/m
  3. 3. T = 1.099 s
  4. 4. T = 3.475 s
  5. 5. amax = 4.154 m/s²
  6. 6. amax = 23.61 m/s²

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