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 kgk = ?

A 2.9 kg mass on a spring makes 30 complete oscillations in 57 s. Find the spring stiffness k.

m = 2.9 kgN = 30t = 57 s
k = N/m
2.Easy
3.7 kgk

A 3.7 kg mass on a spring makes 10 complete oscillations in 13 s. Find the frequency f of the oscillation.

m = 3.7 kgN = 10t = 13 s
f = Hz
3.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
4.Medium
L = 0.6 m

A simple pendulum has a length of 0.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.6 mg = 9.81 m/s²
T = s
5.Hard
3.7 kgk = 60 N/mA = 15 cm

A 3.7 kg mass on a spring with k = 60 N/m is pulled 15 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.7 kgk = 60 N/mA = 15 cm
amax = m/s²
6.Hard
1.7 kgk = 310 N/mA = 11 cm

A 1.7 kg mass on a spring with k = 310 N/m is pulled 11 cm from equilibrium and released. Find its maximum speed vmax.

m = 1.7 kgk = 310 N/mA = 11 cm
vmax = m/s

Answer key

  1. 1. k = 31.71 N/m
  2. 2. f = 0.7692 Hz
  3. 3. T = 3.108 s
  4. 4. T = 1.554 s
  5. 5. amax = 2.432 m/s²
  6. 6. vmax = 1.485 m/s

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