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 = ?

A 1.3 kg mass on a spring makes 25 complete oscillations in 36 s. Find the spring stiffness k.

m = 1.3 kgN = 25t = 36 s
k = N/m
2.Easy
0.1 kgk = ?16.5 cm

Hanging a 0.1 kg mass on a spring stretches it by 16.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 0.1 kgx = 16.5 cmg = 9.81 m/s²
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 = 0.2 m

A simple pendulum has a length of 0.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.2 mg = 9.81 m/s²
T = s
5.Hard
0.2 kgk = 280 N/mA = 15 cm

A 0.2 kg mass on a spring with k = 280 N/m is pulled 15 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.2 kgk = 280 N/mA = 15 cm
amax = m/s²
6.Hard
0.9 kgk = 260 N/mA = 16 cm

A 0.9 kg mass on a spring with k = 260 N/m is pulled 16 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.9 kgk = 260 N/mA = 16 cm
E = J

Answer key

  1. 1. k = 24.75 N/m
  2. 2. k = 5.945 N/m
  3. 3. L = 1.811 m
  4. 4. T = 0.8971 s
  5. 5. amax = 210 m/s²
  6. 6. E = 3.328 J

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