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
1.3 kgk = ?5.5 cm

Hanging a 1.3 kg mass on a spring stretches it by 5.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.3 kgx = 5.5 cmg = 9.81 m/s²
k = N/m
2.Easy
1.6 kgk8.5 cm

Hanging a 1.6 kg mass on a spring stretches it by 8.5 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 = 1.6 kgx = 8.5 cmg = 9.81 m/s²
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.7 s? Use g = 9.81 m/s². Find L.

T = 2.7 sg = 9.81 m/s²
L = m
4.Medium
L = 0.8 m

A simple pendulum has a length of 0.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.8 mg = 9.81 m/s²
T = s
5.Hard
1.2 kgk = 260 N/mA = 15 cm

A 1.2 kg mass on a spring with k = 260 N/m is pulled 15 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.2 kgk = 260 N/mA = 15 cm
amax = m/s²
6.Hard
1.5 kgk = 460 N/mA = 12 cm

A 1.5 kg mass on a spring with k = 460 N/m is pulled 12 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.5 kgk = 460 N/mA = 12 cm
E = J

Answer key

  1. 1. k = 231.9 N/m
  2. 2. T = 0.5849 s
  3. 3. L = 1.811 m
  4. 4. T = 1.794 s
  5. 5. amax = 32.5 m/s²
  6. 6. E = 3.312 J

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