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
3.5 kgk = ?

A 3.5 kg mass on a spring oscillates with a period of 1.55 s. Find the spring stiffness k.

m = 3.5 kgT = 1.55 s
k = N/m
2.Easy
3.1 kgk = ?

A 3.1 kg mass on a spring oscillates with a period of 1.45 s. Find the spring stiffness k.

m = 3.1 kgT = 1.45 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.4 s? Use g = 9.81 m/s². Find L.

T = 1.4 sg = 9.81 m/s²
L = m
4.Medium
L = 2.4 m

A simple pendulum has a length of 2.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.4 mg = 9.81 m/s²
T = s
5.Hard
0.7 kgk = 140 N/mA = 11 cm

A 0.7 kg mass on a spring with k = 140 N/m is pulled 11 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.7 kgk = 140 N/mA = 11 cm
amax = m/s²
6.Hard
0.4 kgk = 470 N/mA = 14 cm

A 0.4 kg mass on a spring with k = 470 N/m is pulled 14 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.4 kgk = 470 N/mA = 14 cm
amax = m/s²

Answer key

  1. 1. k = 57.51 N/m
  2. 2. k = 58.21 N/m
  3. 3. L = 0.487 m
  4. 4. T = 3.108 s
  5. 5. amax = 22 m/s²
  6. 6. amax = 164.5 m/s²

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