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
0.2 kgk = 240 N/m

A 0.2 kg mass on a spring with stiffness 240 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.2 kgk = 240 N/m
f = Hz
2.Easy
2.2 kgk = 400 N/m

A 2.2 kg mass on a spring with stiffness 400 N/m oscillates on a frictionless surface. Find the period T.

m = 2.2 kgk = 400 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1 s? Use g = 9.81 m/s². Find L.

T = 1 sg = 9.81 m/s²
L = m
4.Medium
L = 2.5 m

A simple pendulum has a length of 2.5 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.5 mg = 9.81 m/s²
T = s
5.Hard
1 kgk = 420 N/mA = 13 cm

A 1 kg mass on a spring with k = 420 N/m is pulled 13 cm from equilibrium and released. Find its maximum speed vmax.

m = 1 kgk = 420 N/mA = 13 cm
vmax = m/s
6.Hard
2.2 kgk = 290 N/mA = 20 cm

A 2.2 kg mass on a spring with k = 290 N/m is pulled 20 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.2 kgk = 290 N/mA = 20 cm
amax = m/s²

Answer key

  1. 1. f = 5.513 Hz
  2. 2. T = 0.466 s
  3. 3. L = 0.2485 m
  4. 4. T = 3.172 s
  5. 5. vmax = 2.664 m/s
  6. 6. amax = 26.36 m/s²

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