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
2.9 kgk9 cm

Hanging a 2.9 kg mass on a spring stretches it by 9 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 = 2.9 kgx = 9 cmg = 9.81 m/s²
T = s
2.Easy
2.1 kgk = ?

A 2.1 kg mass on a spring oscillates with a period of 2.5 s. Find the spring stiffness k.

m = 2.1 kgT = 2.5 s
k = N/m
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 = ?

How long must a simple pendulum be to have a period of 2.1 s? Use g = 9.81 m/s². Find L.

T = 2.1 sg = 9.81 m/s²
L = m
5.Hard
1 kgk = 460 N/mA = 2 cm

A 1 kg mass on a spring with k = 460 N/m is pulled 2 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1 kgk = 460 N/mA = 2 cm
amax = m/s²
6.Hard
3.5 kgk = 70 N/mA = 8 cm

A 3.5 kg mass on a spring with k = 70 N/m is pulled 8 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.5 kgk = 70 N/mA = 8 cm
E = J

Answer key

  1. 1. T = 0.6018 s
  2. 2. k = 13.26 N/m
  3. 3. L = 1.811 m
  4. 4. L = 1.096 m
  5. 5. amax = 9.2 m/s²
  6. 6. E = 0.224 J

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